## Standards

CCSS.MATH.CONTENT.HSG.CO.B.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

CCSS.MATH.CONTENT.HSG.CO.C.9 Prove theorems about lines and angles.

CCSS.MATH.CONTENT.HSG.CO.C.10 Prove theorems about triangles.

CCSS.MATH.CONTENT.HSG.CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).

CCSS.MATH.CONTENT.HSG.CO.C.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; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints*.CCSS.MATH.CONTENT.HSG.CO.C.10 Prove theorems about triangles.

*Theorems include: measures of interior angles of a triangle sum to 180°; 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; the medians of a triangle meet at a point*.CCSS.MATH.CONTENT.HSG.CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).

*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*.## Goals

1. The
student will demonstrate the ability to use fundamental concepts of geometry,
including definitions, basic constructions, and tools of geometry.

2. The student will demonstrate the ability to apply the properties of angles, parallel and perpendicular lines.

3. The student will demonstrate the ability to apply definitions and theorems of triangles.

2. The student will demonstrate the ability to apply the properties of angles, parallel and perpendicular lines.

3. The student will demonstrate the ability to apply definitions and theorems of triangles.

## Objectives

1. Draw conclusions about triangles based on congruence statements.2. Draw conclusions about triangles based on congruence postulates.

3. Use triangle congruence and corresponding parts of congruent triangles To prove that parts of two triangles are congruent.

4. Use and apply properties of isosceles and equilateral triangles.

5. Establish connections and relationships amongst concepts learned throughout the chapter.

3. Use triangle congruence and corresponding parts of congruent triangles To prove that parts of two triangles are congruent.

4. Use and apply properties of isosceles and equilateral triangles.

5. Establish connections and relationships amongst concepts learned throughout the chapter.