Learning Goal: Introduce the Triangle Proportionality Theorem while building proficiency with similarity proof and finding missing sides.
- Common Core
- HSG.SRT.A – Understand similarity in terms of similarity transformations
- HSG.SRT.B.4 – Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
- HSG.SRT.B.5 – Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
- G.6(D) – verify theorems about the relationships in triangles, including proof of the Pythagorean Theorem, the sum of interior angles, base angles of isosceles triangles, midsegments, and medians, and apply these relationships to solve problems
- G.7(A) – 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) – apply the Angle-Angle criterion to verify similar triangles and apply the proportionality of the corresponding sides to solve problems
- G.8(A) – prove theorems about similar triangles, including the Triangle Proportionality theorem, and apply these theorems to solve problems