GEOM.MATH.7.B
Apply the Angle-Angle criterion to verify similar triangles and apply the proportionality of the corresponding sides 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
Angle-Angle criterionsimilar trianglesproportionalitycorresponding sidesproblems
Skills
- apply (the Angle-Angle criterion to verify similar triangles) #dok2
- verify (that triangles are similar using the Angle-Angle criterion) #dok2
- apply (proportionality of corresponding sides to solve problems) #dok2
- explain (why the Angle-Angle criterion confirms triangle similarity) #dok3
- solve (problems involving similar triangles and proportional sides) #dok3
Learning Targets
- I can recognize when two triangles satisfy the Angle-Angle similarity criterion. #dok1
- I can state the Angle-Angle criterion for triangle similarity. #dok1
- I can identify corresponding angles and sides of similar triangles. #dok1
- I can apply the Angle-Angle criterion to verify that two triangles are similar. #dok2
- I can use the proportionality of corresponding sides to solve for missing values in similar triangles. #dok2
- I can set up and solve proportions based on similar triangles in real-world and mathematical contexts. #dok2
- I can reason through multi-step problems involving similar triangles and justify my steps. #dok3
- I can explain and defend my reasoning for using the Angle-Angle criterion to establish similarity. #dok3
- I can create and solve problems that require applying the Angle-Angle criterion and proportionality of sides. #dok3
Big Ideas
- Triangles are similar when two of their corresponding angles are congruent, leading to the proportionality of corresponding sides.
- The Angle-Angle criterion for similarity provides a powerful method for solving real-world problems involving indirect measurement and proportional reasoning.
Essential Questions
- How do you know when two triangles are similar?
- Why does having two pairs of congruent angles guarantee triangle similarity?
- How can you use the proportionality of sides in similar triangles to solve for unknown lengths?
- What are some real-world situations where the Angle-Angle criterion can be applied?
- How does triangle similarity help us solve complex geometric problems?