GEOM.MATH.8.A
Prove theorems about similar triangles, including the Triangle Proportionality theorem, and apply these theorems to solve problems.
Geometry · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012
Standard Unwrapping
AI-generated as a starting point — sign in to edit.Vocabulary
theoremsimilar trianglesTriangle Proportionality theoremproblems
Skills
- prove (theorems about similar triangles) #dok3
- apply (theorems about similar triangles to solve problems) #dok2
- explain (Triangle Proportionality theorem and its application) #dok2
- justify (reasoning in proofs of similarity) #dok3
Learning Targets
- I can recall the definitions of similar triangles and the Triangle Proportionality theorem. #dok1
- I can identify pairs of similar triangles in geometric diagrams. #dok1
- I can use the Triangle Proportionality theorem to calculate unknown lengths. #dok2
- I can recognize when triangles are similar based on their sides or angles. #dok2
- I can explain how the Triangle Proportionality theorem is established. #dok2
- I can justify the similarity of triangles using a formal proof. #dok3
- I can prove the Triangle Proportionality theorem using deductive reasoning. #dok3
- I can apply theorems about similar triangles to solve multi-step geometric problems. #dok3
Big Ideas
- Understanding and proving the properties of similar triangles provides a foundation for solving a wide range of geometric problems.
- The Triangle Proportionality theorem and related theorems establish powerful shortcuts for reasoning about proportional relationships in geometry.
Essential Questions
- How can you determine whether two triangles are similar?
- What is the Triangle Proportionality theorem and how is it proven?
- How can you apply properties of similar triangles to solve for unknown lengths?
- Why is proving geometric theorems about similarity important in mathematics?
- In what real-world situations might you use properties of similar triangles?