**Title:** Characteristics of Quadrilaterals

**Description:**
Students will begin unit on quadrilaterals with basic overview of characteristics of parallelograms, rectangles, squares, rhombi, and isosceles and non-isosceles trapezoids. After the word wall is made, the teacher can use interactive websites to reinforce concepts.
**Standard(s): **

[MA2015] GEO (9-12) 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.* [G-CO11]

**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 non-isosceles trapezoids. After the word wall is made, the teacher can use interactive websites to reinforce concepts.

**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): **

[MA2015] GEO (9-12) 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). [G-GPE5]

**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.

**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 "line-up" of twelve suspects (different quadrilaterals with their properties). The students must decide which suspect(s) from the line-up meets the description. The "guilty" quadrilateral will be discovered at the end of the activity.
**Standard(s): **

**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 "line-up" of twelve suspects (different quadrilaterals with their properties). The students must decide which suspect(s) from the line-up meets the description. The "guilty" quadrilateral will be discovered at the end of the activity.

**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): **

[MA2015] GEO (9-12) 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.* [G-CO11]

**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

**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): **

[MA2015] GEO (9-12) 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.* [G-CO11]

**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

**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): **

[MA2015] GEO (9-12) 11: Prove theorems about parallelograms.

**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

**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): **

[MA2015] GEO (9-12) 11: Prove theorems about parallelograms.

**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

**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): **

[MA2015] GEO (9-12) 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

**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): **

[MA2015] GEO (9-12) 13: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. [G-CO13]

**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

**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): **

[MA2015] GEO (9-12) 11: Prove theorems about parallelograms.

**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

**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): **

[MA2015] GEO (9-12) 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.* [G-CO12]

**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

**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): **

[MA2015] GEO (9-12) 11: Prove theorems about parallelograms.

**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