Curriculum / Math / 10th Grade / Unit 3: Dilations and Similarity / Lesson 15

Dilations and Similarity

Lesson 15

Math

Unit 3

10th Grade

Lesson 15 of 18

Objective

Develop the angle bisector theorem based on facts about similarity and congruence, and use this in the solution of problems.

Lesson Map

Topic A: Dilations off the Coordinate Plane

Lesson

Describe properties of scale drawings.

Standards

G.SRT.A.2

Lesson

Define and describe the characteristics of dilations. Dilate figures using constructions when the center of dilation is not on the figure.

Standards

G.CO.A.2G.SRT.A.2G.SRT.A.3

Lesson

Verify that dilations result in congruent angles and proportional line segments.

Standards

G.SRT.A.2

Lesson

Divide a line segment into equal sections using dilation.

Standards

G.CO.D.12G.SRT.A.1.AG.SRT.A.1.B

Lesson

Dilate a figure from a point on the figure. Use the properties of dilations with respect to parallel lines to verify dilations and find the center of dilation.

Standards

G.CO.D.12G.SRT.A.1.AG.SRT.A.2

Lesson

Prove that a line parallel to one side of a triangle divides the other two sides proportionally.

Standards

G.CO.C.10G.SRT.B.4G.SRT.B.5

Lesson

Identify measurements in dilated figures with the center of dilation on the figure directly and algebraically.

Standards

G.SRT.A.2

Topic B: Dilations on the Coordinate Plane

Lesson

Dilate a figure on the coordinate plane when the center of dilation is the origin.

Standards

G.CO.A.2G.SRT.A.2

Lesson

Dilate a figure when the center of dilation is not the origin. Determine center of dilation given the original and dilated figure.

Standards

G.CO.A.2G.SRT.A.2

Topic C: Defining Similarity

Lesson

Define similarity transformation as the composition of basic rigid motions and dilations. Describe similarity transformation applied to an arbitrary figure.

Standards

G.SRT.A.2G.SRT.B.5

Lesson

Prove that all circles are similar.

Standards

G.C.A.1

Lesson

Prove angle-angle criterion for two triangles to be similar.

Standards

G.SRT.A.3

Lesson

Use angle-angle criterion to prove two triangles to be similar.