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Title: Characteristics of Quadrilaterals
Description:
Students will begin unit on quadrilaterals with basic overview of characteristics of parallelograms, rectangles, squares, rhombi, and isosceles and nonisosceles trapezoids. After the word wall is made, the teacher can use interactive websites to reinforce concepts.
Standard(s): [MA2013] GEO (912) 11: Prove theorems about parallelograms. Theorems include opposite sides are congruent, opposite angles are congruent; the diagonals of a parallelogram bisect each other; and conversely, rectangles are parallelograms with congruent diagonals. [GCO11]
Subject: Mathematics (9  12)
Title: Characteristics of Quadrilaterals
Description: Students will begin unit on quadrilaterals with basic overview of characteristics of parallelograms, rectangles, squares, rhombi, and isosceles and nonisosceles trapezoids. After the word wall is made, the teacher can use interactive websites to reinforce concepts.
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Title: What do we have in Common? Discover the properties of the diagonals of quadrilaterals.
Description:
This inquiry lesson explores the definitions of quadrilaterals and the properties of the diagonals of quadrilaterals to classify quadrilaterals. Students will work cooperatively to justify conclusions.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
Standard(s): [MA2013] GEO (912) 11: Prove theorems about parallelograms. Theorems include opposite sides are congruent, opposite angles are congruent; the diagonals of a parallelogram bisect each other; and conversely, rectangles are parallelograms with congruent diagonals. [GCO11] [MA2013] GEO (912) 31: Prove the slope criteria for parallel and perpendicular lines, and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). [GGPE5]
Subject: Mathematics (9  12)
Title: What do we have in Common? Discover the properties of the diagonals of quadrilaterals.
Description: This inquiry lesson explores the definitions of quadrilaterals and the properties of the diagonals of quadrilaterals to classify quadrilaterals. Students will work cooperatively to justify conclusions.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
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Title: Quadrilaterals
Description:
This is an inquiry lesson used to review Algebra 1 objectives by applying them to geometry concepts. Students explore the properties of quadrilaterals and classify them by definition. This lesson can be use in geometry classes. Students in geometry classes can apply theorems and definitions of quadrilaterals rather than as an inquiry lesson.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Standard(s): [MA2013] AL1 (912) 20: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. [AREI6] [MA2013] AL1 (912) 24: Graph the solutions to a linear inequality in two variables as a halfplane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding halfplanes. [AREI12] [MA2013] GEO (912) 1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc. [GCO1] [MA2013] GEO (912) 9: Prove theorems about lines and angles. Theorems include vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; and points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints. [GCO9] [MA2013] GEO (912) 11: Prove theorems about parallelograms. Theorems include opposite sides are congruent, opposite angles are congruent; the diagonals of a parallelogram bisect each other; and conversely, rectangles are parallelograms with congruent diagonals. [GCO11] [MA2013] GEO (912) 30: Use coordinates to prove simple geometric theorems algebraically. [GGPE4] [MA2013] GEO (912) 31: Prove the slope criteria for parallel and perpendicular lines, and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). [GGPE5] [MA2013] GEO (912) 33: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.* [GGPE7] [MA2013] GEO (912) 34: Determine areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics. (Alabama) [MA2013] (8) 23: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [8G8] [MA2013] GEO (912) 1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc. [GCO1] [MA2013] (8) 23: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [8G8] [MA2013] GEO (912) 1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc. [GCO1]
Subject: Mathematics (8  12)
Title: Quadrilaterals
Description: This is an inquiry lesson used to review Algebra 1 objectives by applying them to geometry concepts. Students explore the properties of quadrilaterals and classify them by definition. This lesson can be use in geometry classes. Students in geometry classes can apply theorems and definitions of quadrilaterals rather than as an inquiry lesson.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
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Title: Trapezoids: What's Equal or Right About Them?
Description:
This lesson will examine the properties of two trapezoids  isosceles and right. The lesson will then use the properties to solve deeper analytical problems.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Standard(s): [MA2013] (7) 12: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. [7G2] [MA2013] GEO (912) 1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc. [GCO1] [MA2013] GEO (912) 11: Prove theorems about parallelograms. Theorems include opposite sides are congruent, opposite angles are congruent; the diagonals of a parallelogram bisect each other; and conversely, rectangles are parallelograms with congruent diagonals. [GCO11]
Subject: Mathematics (7  12)
Title: Trapezoids: What's Equal or Right About Them?
Description: This lesson will examine the properties of two trapezoids  isosceles and right. The lesson will then use the properties to solve deeper analytical problems.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
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Title: Geometrica Fights Back!
Description:
This activity is designed to give students practice with the properties of special quadrilaterals (parallelograms, rectangles, rhombuses, squares, trapezoids, and kites). The students are provided with a "murder mystery" sheet with descriptions of each "suspect" and a "lineup" of twelve suspects (different quadrilaterals with their properties). The students must decide which suspect(s) from the lineup meets the description. The "guilty" quadrilateral will be discovered at the end of the activity.
Standard(s): [MA2013] GEO (912) 11: Prove theorems about parallelograms. Theorems include opposite sides are congruent, opposite angles are congruent; the diagonals of a parallelogram bisect each other; and conversely, rectangles are parallelograms with congruent diagonals. [GCO11]
Subject: Mathematics (9  12)
Title: Geometrica Fights Back!
Description: This activity is designed to give students practice with the properties of special quadrilaterals (parallelograms, rectangles, rhombuses, squares, trapezoids, and kites). The students are provided with a "murder mystery" sheet with descriptions of each "suspect" and a "lineup" of twelve suspects (different quadrilaterals with their properties). The students must decide which suspect(s) from the lineup meets the description. The "guilty" quadrilateral will be discovered at the end of the activity.
Thinkfinity Lesson Plans
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Title: Diagonals to Quadrilaterals
Description:
In this Illuminations lesson, students start with the diagonals and deduce the type of quadrilateral that surrounds them. Using an applet, students explore certain characteristics of diagonals and the quadrilaterals that are associated with them.
Standard(s): [MA2013] GEO (912) 11: Prove theorems about parallelograms. Theorems include opposite sides are congruent, opposite angles are congruent; the diagonals of a parallelogram bisect each other; and conversely, rectangles are parallelograms with congruent diagonals. [GCO11]
Subject: Mathematics Title: Diagonals to Quadrilaterals
Description: In this Illuminations lesson, students start with the diagonals and deduce the type of quadrilateral that surrounds them. Using an applet, students explore certain characteristics of diagonals and the quadrilaterals that are associated with them. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Diagonals and Quadrilaterals Overhead
Description:
This reproducible transparency, from an Illuminations lesson, is used to record students' findings as they explain which quadrilaterals are possible with different diagonal relationships.
Standard(s): [MA2013] GEO (912) 11: Prove theorems about parallelograms. Theorems include opposite sides are congruent, opposite angles are congruent; the diagonals of a parallelogram bisect each other; and conversely, rectangles are parallelograms with congruent diagonals. [GCO11]
Subject: Mathematics Title: Diagonals and Quadrilaterals Overhead
Description: This reproducible transparency, from an Illuminations lesson, is used to record students' findings as they explain which quadrilaterals are possible with different diagonal relationships. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Think of a Quadrilateral
Description:
This reproducible transparency, from an Illuminations lesson, asks students to draw and describe a quadrilateral constructed from two perpendicular diagonals.
Standard(s): [MA2013] GEO (912) 11: Prove theorems about parallelograms. Theorems include opposite sides are congruent, opposite angles are congruent; the diagonals of a parallelogram bisect each other; and conversely, rectangles are parallelograms with congruent diagonals. [GCO11]
Subject: Mathematics Title: Think of a Quadrilateral
Description: This reproducible transparency, from an Illuminations lesson, asks students to draw and describe a quadrilateral constructed from two perpendicular diagonals. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Diagonals and Quadrilaterals Answer Key
Description:
This reproducible answer sheet, from an Illuminations lesson, contains sample results and conclusions for an activity in which students explain which quadrilaterals are possible with different diagonal relationships.
Standard(s): [MA2013] GEO (912) 11: Prove theorems about parallelograms. Theorems include opposite sides are congruent, opposite angles are congruent; the diagonals of a parallelogram bisect each other; and conversely, rectangles are parallelograms with congruent diagonals. [GCO11]
Subject: Mathematics Title: Diagonals and Quadrilaterals Answer Key
Description: This reproducible answer sheet, from an Illuminations lesson, contains sample results and conclusions for an activity in which students explain which quadrilaterals are possible with different diagonal relationships. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Pinwheel
Description:
In this Illuminations lesson, students create parallelograms from square sheets of paper and connect them to form an octagon. During the construction, students consider angle measures, segment lengths, and areas in terms of the original square. At the end of the lesson, the octagon is transformed into a pinwheel, and students discover a surprising result. There is also a link to a related activity sheet.
Standard(s): [MA2013] GEO (912) 3: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. [GCO3] [MA2013] GEO (912) 11: Prove theorems about parallelograms. Theorems include opposite sides are congruent, opposite angles are congruent; the diagonals of a parallelogram bisect each other; and conversely, rectangles are parallelograms with congruent diagonals. [GCO11] [MA2013] GEO (912) 33: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.* [GGPE7] [MA2013] GEO (912) 34: Determine areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics. (Alabama)
Subject: Mathematics Title: Pinwheel
Description: In this Illuminations lesson, students create parallelograms from square sheets of paper and connect them to form an octagon. During the construction, students consider angle measures, segment lengths, and areas in terms of the original square. At the end of the lesson, the octagon is transformed into a pinwheel, and students discover a surprising result. There is also a link to a related activity sheet. Thinkfinity Partner: Illuminations Grade Span: 6,7,8,9,10,11,12
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Title: All in the Family
Description:
In this Illuminations lesson, students use a dynamic geometry applet to conjecture about the relationships between characteristics of a square: side length, diagonal length, perimeter, and area. Students use graphs to represent functional relationships between two characteristics, such as diagonal length as a function of perimeter. In addition, there are links to online activities, reproducibles, and other related resources.
Standard(s): [MA2013] GEO (912) 11: Prove theorems about parallelograms. Theorems include opposite sides are congruent, opposite angles are congruent; the diagonals of a parallelogram bisect each other; and conversely, rectangles are parallelograms with congruent diagonals. [GCO11] [MA2013] GEO (912) 13: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. [GCO13]
Subject: Mathematics Title: All in the Family
Description: In this Illuminations lesson, students use a dynamic geometry applet to conjecture about the relationships between characteristics of a square: side length, diagonal length, perimeter, and area. Students use graphs to represent functional relationships between two characteristics, such as diagonal length as a function of perimeter. In addition, there are links to online activities, reproducibles, and other related resources. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Diagonals to Quadrilaterals
Description:
This lesson provides a unique opportunity for students to start with the diagonals and deduce the type of quadrilateral that surrounds them. Using an applet, students explore certain characteristics of diagonals and the quadrilaterals that are associated with them.
Standard(s): [MA2013] GEO (912) 11: Prove theorems about parallelograms. Theorems include opposite sides are congruent, opposite angles are congruent; the diagonals of a parallelogram bisect each other; and conversely, rectangles are parallelograms with congruent diagonals. [GCO11]
Diagonals to Quadrilaterals
http://illuminations...
This lesson provides a unique opportunity for students to start with the diagonals and deduce the type of quadrilateral that surrounds them. Using an applet, students explore certain characteristics of diagonals and the quadrilaterals that are associated with them.
Interactives/Games
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Title: Geometry StepbyStep
Description:
This site provides a mix of sound, science, and Incan history in order to raise students' interest in Euclidean geometry. Visitors will find geometry problems, proofs, quizzes, puzzles, quotations, visual displays, "scientific speculation", and more.
Standard(s): [MA2013] GEO (912) 1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc. [GCO1] [MA2013] GEO (912) 5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. [GCO5] [MA2013] GEO (912) 7: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. [GCO7] [MA2013] GEO (912) 8: Explain how the criteria for triangle congruence, anglesideangle (ASA), sideangleside (SAS), and sidesideside (SSS), follow from the definition of congruence in terms of rigid motions. [GCO8] [MA2013] GEO (912) 9: Prove theorems about lines and angles. Theorems include vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; and points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints. [GCO9] [MA2013] GEO (912) 10: Prove theorems about triangles. Theorems include measures of interior angles of a triangle sum to 180^{o}, base angles of isosceles triangles are congruent, the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length, and the medians of a triangle meet at a point. [GCO10] [MA2013] GEO (912) 11: Prove theorems about parallelograms. Theorems include opposite sides are congruent, opposite angles are congruent; the diagonals of a parallelogram bisect each other; and conversely, rectangles are parallelograms with congruent diagonals. [GCO11] [MA2013] GEO (912) 12: Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software. Constructions include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. [GCO12] [MA2013] GEO (912) 13: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. [GCO13] [MA2013] GEO (912) 16: Use the properties of similarity transformations to establish the angleangle (AA) criterion for two triangles to be similar. [GSRT3] [MA2013] GEO (912) 17: Prove theorems about triangles. Theorems include a line parallel to one side of a triangle divides the other two proportionally, and conversely; and the Pythagorean Theorem proved using triangle similarity. [GSRT4] [MA2013] GEO (912) 18: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. [GSRT5] [MA2013] GEO (912) 19: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle leading to definitions of trigonometric ratios for acute angles. [GSRT6] [MA2013] GEO (912) 20: Explain and use the relationship between the sine and cosine of complementary angles. [GSRT7] [MA2013] GEO (912) 21: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.* [GSRT8] [MA2013] GEO (912) 22: (+) Prove the Law of Sines and the Law of Cosines and use them to solve problems. [GSRT10] [MA2013] GEO (912) 23: (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and nonright triangles (e.g., surveying problems, resultant forces).
[GSRT11] [MA2013] GEO (912) 24: Prove that all circles are similar. [GC1] [MA2013] GEO (912) 25: Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. [GC2] [MA2013] GEO (912) 26: Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. [GC3] [MA2013] GEO (912) 27: (+) Construct a tangent line from a point outside a given circle to the circle. [GC4] [MA2013] GEO (912) 28: Derive, using similarity, the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. [GC5] [MA2013] GEO (912) 29: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. [GGPE1] [MA2013] GEO (912) 35: Give an informal argument for the formulas for the circumference of a circle; area of a circle; and volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments. [GGMD1] [MA2013] GEO (912) 37: Determine the relationship between surface areas of similar figures and volumes of similar figures. (Alabama)
Geometry StepbyStep
http://agutie.homest...
This site provides a mix of sound, science, and Incan history in order to raise students' interest in Euclidean geometry. Visitors will find geometry problems, proofs, quizzes, puzzles, quotations, visual displays, "scientific speculation", and more.
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Title: Geometry StepbyStep
Description:
This site provides a mix of sound, science, and Incan history in order to raise students' interest in Euclidean geometry. Visitors will find geometry problems, proofs, quizzes, puzzles, quotations, visual displays, "scientific speculation", and more.
Standard(s): [MA2013] GEO (912) 1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc. [GCO1] [MA2013] GEO (912) 5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. [GCO5] [MA2013] GEO (912) 7: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. [GCO7] [MA2013] GEO (912) 8: Explain how the criteria for triangle congruence, anglesideangle (ASA), sideangleside (SAS), and sidesideside (SSS), follow from the definition of congruence in terms of rigid motions. [GCO8] [MA2013] GEO (912) 9: Prove theorems about lines and angles. Theorems include vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; and points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints. [GCO9] [MA2013] GEO (912) 10: Prove theorems about triangles. Theorems include measures of interior angles of a triangle sum to 180^{o}, base angles of isosceles triangles are congruent, the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length, and the medians of a triangle meet at a point. [GCO10] [MA2013] GEO (912) 11: Prove theorems about parallelograms. Theorems include opposite sides are congruent, opposite angles are congruent; the diagonals of a parallelogram bisect each other; and conversely, rectangles are parallelograms with congruent diagonals. [GCO11] [MA2013] GEO (912) 12: Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software. Constructions include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. [GCO12] [MA2013] GEO (912) 13: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. [GCO13] [MA2013] GEO (912) 16: Use the properties of similarity transformations to establish the angleangle (AA) criterion for two triangles to be similar. [GSRT3] [MA2013] GEO (912) 17: Prove theorems about triangles. Theorems include a line parallel to one side of a triangle divides the other two proportionally, and conversely; and the Pythagorean Theorem proved using triangle similarity. [GSRT4] [MA2013] GEO (912) 18: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. [GSRT5] [MA2013] GEO (912) 19: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle leading to definitions of trigonometric ratios for acute angles. [GSRT6] [MA2013] GEO (912) 20: Explain and use the relationship between the sine and cosine of complementary angles. [GSRT7] [MA2013] GEO (912) 21: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.* [GSRT8] [MA2013] GEO (912) 22: (+) Prove the Law of Sines and the Law of Cosines and use them to solve problems. [GSRT10] [MA2013] GEO (912) 23: (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and nonright triangles (e.g., surveying problems, resultant forces).
[GSRT11] [MA2013] GEO (912) 24: Prove that all circles are similar. [GC1] [MA2013] GEO (912) 25: Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. [GC2] [MA2013] GEO (912) 26: Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. [GC3] [MA2013] GEO (912) 27: (+) Construct a tangent line from a point outside a given circle to the circle. [GC4] [MA2013] GEO (912) 28: Derive, using similarity, the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. [GC5] [MA2013] GEO (912) 29: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. [GGPE1] [MA2013] GEO (912) 35: Give an informal argument for the formulas for the circumference of a circle; area of a circle; and volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments. [GGMD1] [MA2013] GEO (912) 37: Determine the relationship between surface areas of similar figures and volumes of similar figures. (Alabama)
Geometry StepbyStep
http://agutie.homest...
This site provides a mix of sound, science, and Incan history in order to raise students' interest in Euclidean geometry. Visitors will find geometry problems, proofs, quizzes, puzzles, quotations, visual displays, "scientific speculation", and more.
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Title: Geometry StepbyStep
Description:
This site provides a mix of sound, science, and Incan history in order to raise students' interest in Euclidean geometry. Visitors will find geometry problems, proofs, quizzes, puzzles, quotations, visual displays, "scientific speculation", and more.
Standard(s): [MA2013] GEO (912) 1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc. [GCO1] [MA2013] GEO (912) 5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. [GCO5] [MA2013] GEO (912) 7: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. [GCO7] [MA2013] GEO (912) 8: Explain how the criteria for triangle congruence, anglesideangle (ASA), sideangleside (SAS), and sidesideside (SSS), follow from the definition of congruence in terms of rigid motions. [GCO8] [MA2013] GEO (912) 9: Prove theorems about lines and angles. Theorems include vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; and points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints. [GCO9] [MA2013] GEO (912) 10: Prove theorems about triangles. Theorems include measures of interior angles of a triangle sum to 180^{o}, base angles of isosceles triangles are congruent, the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length, and the medians of a triangle meet at a point. [GCO10] [MA2013] GEO (912) 11: Prove theorems about parallelograms. Theorems include opposite sides are congruent, opposite angles are congruent; the diagonals of a parallelogram bisect each other; and conversely, rectangles are parallelograms with congruent diagonals. [GCO11] [MA2013] GEO (912) 12: Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software. Constructions include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. [GCO12] [MA2013] GEO (912) 13: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. [GCO13] [MA2013] GEO (912) 16: Use the properties of similarity transformations to establish the angleangle (AA) criterion for two triangles to be similar. [GSRT3] [MA2013] GEO (912) 17: Prove theorems about triangles. Theorems include a line parallel to one side of a triangle divides the other two proportionally, and conversely; and the Pythagorean Theorem proved using triangle similarity. [GSRT4] [MA2013] GEO (912) 18: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. [GSRT5] [MA2013] GEO (912) 19: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle leading to definitions of trigonometric ratios for acute angles. [GSRT6] [MA2013] GEO (912) 20: Explain and use the relationship between the sine and cosine of complementary angles. [GSRT7] [MA2013] GEO (912) 21: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.* [GSRT8] [MA2013] GEO (912) 22: (+) Prove the Law of Sines and the Law of Cosines and use them to solve problems. [GSRT10] [MA2013] GEO (912) 23: (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and nonright triangles (e.g., surveying problems, resultant forces).
[GSRT11] [MA2013] GEO (912) 24: Prove that all circles are similar. [GC1] [MA2013] GEO (912) 25: Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. [GC2] [MA2013] GEO (912) 26: Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. [GC3] [MA2013] GEO (912) 27: (+) Construct a tangent line from a point outside a given circle to the circle. [GC4] [MA2013] GEO (912) 28: Derive, using similarity, the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. [GC5] [MA2013] GEO (912) 29: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. [GGPE1] [MA2013] GEO (912) 35: Give an informal argument for the formulas for the circumference of a circle; area of a circle; and volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments. [GGMD1] [MA2013] GEO (912) 37: Determine the relationship between surface areas of similar figures and volumes of similar figures. (Alabama)
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This site provides a mix of sound, science, and Incan history in order to raise students' interest in Euclidean geometry. Visitors will find geometry problems, proofs, quizzes, puzzles, quotations, visual displays, "scientific speculation", and more.
Thinkfinity Learning Activities
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Title: IGD: Area of a Parallelogram
Description:
This student interactive, from Illuminations, helps students understand and investigate how to find the area of the parallelogram if they already know how to find the area of a rectangle. Students divide the parallelogram into pieces, arrange them together to form a rectangle, and then use the formula for the area of a rectangle to find the area of the parallelogram.
Standard(s): [MA2013] (3) 22: Relate area to the operations of multiplication and addition. [3MD7] [MA2013] (3) 25: Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. [3G2] [MA2013] (6) 21: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld and mathematical problems. [6G1] [MA2013] GEO (912) 11: Prove theorems about parallelograms. Theorems include opposite sides are congruent, opposite angles are congruent; the diagonals of a parallelogram bisect each other; and conversely, rectangles are parallelograms with congruent diagonals. [GCO11]
Subject: Mathematics Title: IGD: Area of a Parallelogram
Description: This student interactive, from Illuminations, helps students understand and investigate how to find the area of the parallelogram if they already know how to find the area of a rectangle. Students divide the parallelogram into pieces, arrange them together to form a rectangle, and then use the formula for the area of a rectangle to find the area of the parallelogram. Thinkfinity Partner: Illuminations Grade Span: 3,4,5,6,7,8
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Title: Interactive Geometry Dictionary: Areas in Geometry
Description:
This student interactive, from Illuminations, demonstrates how to find the area of three common shapes. Interactive investigations demonstrate finding the area of a rectangle, parallelogram, and triangle.
Standard(s): [MA2013] (3) 20: Recognize area as an attribute of plane figures, and understand concepts of area measurement. [3MD5] [MA2013] (3) 21: Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). [3MD6] [MA2013] (3) 22: Relate area to the operations of multiplication and addition. [3MD7] [MA2013] (4) 21: Apply the area and perimeter formulas for rectangles in realworld and mathematical problems. [4MD3] [MA2013] (6) 21: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld and mathematical problems. [6G1] [MA2013] GEO (912) 11: Prove theorems about parallelograms. Theorems include opposite sides are congruent, opposite angles are congruent; the diagonals of a parallelogram bisect each other; and conversely, rectangles are parallelograms with congruent diagonals. [GCO11] [MA2013] GEO (912) 12: Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software. Constructions include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. [GCO12]
Subject: Mathematics Title: Interactive Geometry Dictionary: Areas in Geometry
Description: This student interactive, from Illuminations, demonstrates how to find the area of three common shapes. Interactive investigations demonstrate finding the area of a rectangle, parallelogram, and triangle. Thinkfinity Partner: Illuminations Grade Span: 3,4,5,6,7,8
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Title: Shape Sorter Tool
Description:
This student interactive, from Illuminations, allows students to sort shapes based on their properties using a Venn diagram. Students can choose from various arrangements of Venn diagrams, including those with two or three circles and then place different shapes on their chosen diagram.
Standard(s): [MA2013] GEO (912) 11: Prove theorems about parallelograms. Theorems include opposite sides are congruent, opposite angles are congruent; the diagonals of a parallelogram bisect each other; and conversely, rectangles are parallelograms with congruent diagonals. [GCO11]
Subject: Mathematics Title: Shape Sorter Tool
Description: This student interactive, from Illuminations, allows students to sort shapes based on their properties using a Venn diagram. Students can choose from various arrangements of Venn diagrams, including those with two or three circles and then place different shapes on their chosen diagram. Thinkfinity Partner: Illuminations Grade Span: 6,7,8

