Geometry Unit 8

Big Idea:

Use dilations to understand and prove the similarity of polygons

Student Expectations:

Priority TEKS

G.8(A) [Supporting] prove theorems about similar triangles, including the Triangle Proportionality theorem, and apply these theorems to solve problems

Focus TEKS

G.3(B) [Readiness] determine the image or pre-image of a given two-dimensional figure under a composition of rigid transformations, a composition of non-rigid transformations, and a composition of both, including dilations where the center can be any point in the plane

G.7(A) [Supporting] apply the definition of similarity in terms of a dilation to identify similar figures and their proportional sides and the congruent corresponding angles

G.7(B) [Readiness] apply the Angle-Angle criterion to verify similar triangles and apply the proportionality of the corresponding sides to solve problems

G.8(B) [Supporting] identify and apply the relationships that exist when an altitude is drawn to the hypotenuse of a right triangle, including the geometric mean, to solve problems

Ongoing TEKS

G.3(A) [Supporting] describe and perform transformations of figures in a plane using coordinate notation

G.3(B) [Readiness] determine the image or pre-image of a given two-dimensional figure under a composition of rigid transformations, a composition of non-rigid transformations, and a composition of both, including dilations where the center can be any point in the plane

G.3(C) [Supporting] identify the sequence of transformations that will carry a given pre-image onto an image on and off the coordinate plane

Student Learning Targets:

• I will perform and describe dilations on and off the coordinate plane.
• I will use similarity transformations to determine whether figures are similar.
• I will identify and apply properties of similarity.
• I will develop criteria for triangles similarity.
• I will prove the AA similarity criterion.
• I will differentiate between SSS and SAS Theorems t prove similarity versus congruence.
• I will write and interpret a similarity statement based on the face that similar triangles have congruent corresponding angles and proportional corresponding sides.
• I will prove triangles and similar.
• I will use similar triangles to solve problems.
• I will redraw transformed similar figures to the same orientations.
• I will prove and apply the Triangle Proportionality Theorem and its converse.

Essential Questions:

• How are congruence and similarity related?
• What types of problem solving applications are enhanced by similar relationships?

Extra Information:

Adopted Textbook: Springboard - Geometry Texas Edition

District Grading Policy

Texas Gateway Online Resource Center