Students begin this first module with Topic A, Constructions. Major constructions include an equilateral triangle, an angle bisector, and a perpendicular bisector. Students synthesize their knowledge of geometric terms with the use of new tools and simultaneously practice precise use of language and efficient communication when they write the steps that accompany each construction (G.CO.1).

Content Standard(s):

Mathematics MA2015 (2016) Grade: 9-12 Geometry

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]

Alabama Alternate Achievement Standards

AAS Standard: M.G.AAS.HS.12- Given a drawing with angles and a protractor overlay, determine which angles are congruent. Sample image below.
Image

Mathematics MA2015 (2016) Grade: 9-12 Geometry

13 ) Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. [G-CO13]

Alabama Alternate Achievement Standards

AAS Standard: M.G.AAS.HS.13- Identify an equilateral triangle from a set of triangles or identify a regular hexagon from a set of hexagons. Make sure sides/angles are marked so that students can identify congruence.

Mathematics MA2019 (2019) Grade: 9-12 Geometry with Data Analysis

30. Develop and use precise definitions of figures such as angle, circle, perpendicular lines, parallel lines, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

Unpacked Content

Evidence Of Student Attainment:

Students:
Given undefined notions of point, line, distance along a line, and distance around a circular arc,

Develop precise definitions of angle, circle, perpendicular line, parallel line, and line segment.

Identify examples and non-examples of angles, circles, perpendicular lines, parallel lines, and line segments.

Teacher Vocabulary:

Point

Line

Segment

Angle

Perpendicular line

Parallel line

Distance

Arc length

Ray

Vertex

Endpoint

Plane

Collinear

Coplanar

Skew

Knowledge:

Students know:

Undefined notions of point, line, distance along a line, and distance around a circular arc.

Properties of a mathematical definition, i.e., the smallest amount of information and properties that are enough to determine the concept. (Note: may not include all information related to concept).

Skills:

Students are able to:

Use known and developed definitions and logical connections to develop new definitions.

Understanding:

Students understand that:

Geometric definitions are developed from a few undefined notions by a logical sequence of connections that lead to a precise definition,
A precise definition should allow for the inclusion of all examples of the concept, and require the exclusion of all non-examples.

Diverse Learning Needs:

Essential Skills:

Learning Objectives: GEO.30.1: Define angle, circle, perpendicular line, parallel line, line segment, and distance.
GEO.30.2: Describe angle, circle, perpendicular line, parallel line, line segment, and distance.
GEO.30.3: Illustrate a point, line, distance along a line, and distance around a circular arc.
GEO.30.4: Identify angle, circle, perpendicular line, parallel line, line segment, and distance.

Define supplementary, complementary, vertical, and adjacent angles; and parallel, perpendicular, and intersecting lines.

Identify all types of angles.

Identify right angles and straight angles.

Demonstrate how to use a protractor to draw an angle.

Define vertices.

Alabama Alternate Achievement Standards

AAS Standard: M.G.AAS.10.30 Demonstrate perpendicular lines, parallel lines, line segments, angles, and circles by drawing, modeling, identifying or creating.