Curriculum / Math / 10th Grade / Unit 2: Congruence in Two Dimensions / Lesson 18

Congruence in Two Dimensions

Lesson 18

Math

Unit 2

10th Grade

Lesson 18 of 18

Objective

Prove theorems about the diagonals of parallelograms.

Lesson Map

Topic A: Introduction to Polygons

Lesson

Define polygon and identify properties of polygons.

Standards

G.CO.A.1G.CO.C.11

Lesson

Prove interior and exterior angle relationships in triangles.

Standards

G.CO.C.10

Lesson

Describe and apply the sum of interior and exterior angles of polygons.

Standards

G.CO.C.11

Topic B: Rigid Motion Congruence of Two-Dimensional Figures

Lesson

Determine congruence of two dimensional figures by translation.

Standards

G.CO.A.2G.CO.A.4G.CO.A.5G.CO.B.7

Lesson

Reflect two dimensional figures on and off the coordinate plane.

Standards

G.CO.A.2G.CO.A.3G.CO.A.5G.CO.B.7

Lesson

Rotate two dimensional figures on and off the coordinate plane.

Standards

G.CO.A.2G.CO.A.3G.CO.A.5G.CO.B.7

Lesson

Describe a sequence of rigid motions that map a pre-image to an image (specifically triangles, rectangles, parallelograms, and regular polygons).

Standards

G.CO.A.5G.CO.B.6

Lesson

Describe single rigid motions, or sequences of rigid motions that have the same effect on a figure.

Standards

G.CO.A.3G.CO.A.5G.CO.B.6

Topic C: Triangle Congruence

Lesson

Develop the Side Angle Side criteria for congruent triangles through rigid motions.

Standards

G.CO.B.7G.CO.B.8

Lesson

Prove angle relationships using the Side Angle Side criteria.

Standards

G.SRT.B.5

Lesson

Prove and apply that the points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.

Standards

G.CO.A.2G.CO.C.10G.CO.C.9

Lesson

Develop Angle, Side, Angle (ASA) and Side, Side, Side (SSS) congruence criteria. Describe how the criteria develop from rigid motions.

Standards

G.CO.B.7G.CO.B.8

Lesson

Use triangle congruence criteria, rigid motions, and other properties of lines and angles to prove congruence between different triangles.

Standards

G.SRT.B.5

Lesson

Prove triangles congruent using Angle, Angle, Side (AAS), and describe why AAA is not a congruency criteria.

Standards

G.CO.B.7G.CO.B.8G.CO.C.10

Lesson

Develop the Hypotenuse- Leg (HL) criteria, and describe the features of a triangle that are necessary to use the HL criteria.

Standards

G.CO.B.7G.CO.C.10

Lesson

Use criteria for triangle congruence to prove relationships among angles and sides in geometric problems.

Standards

G.CO.C.9G.SRT.B.5

Topic D: Parallelogram Properties from Triangle Congruence

Lesson

Prove that the opposite sides and opposite angles of a parallelogram are congruent.

Standards

G.CO.C.11

Lesson

Prove theorems about the diagonals of parallelograms.

Standards

G.CO.C.11

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