Question
What is required for two triangles to be similar? A. 1. The corresponding angles are congruent 2. The corresponding sides are proportional B. 1. The corresponding angles are congruent 2. The corresponding sides are congruent C. 1. The corresponding angles are proportional 2. The corresponding sides are congruent D. 1. The corresponding angles are proportional 2. The corresponding sides are proportional
Ask by Kelly Garrett. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
For two triangles to be similar, their corresponding angles must be congruent and their corresponding sides must be proportional.
Solution
For two triangles to be similar, the following conditions must be met:
1. The corresponding angles of the two triangles must be congruent.
2. The corresponding sides of the two triangles must be proportional.
This means that the correct answer is:
**A. 1. The corresponding angles are congruent 2. The corresponding sides are proportional**.
This is known as the Angle-Angle (AA) similarity criterion, which states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar. Additionally, the proportionality of the sides ensures that the triangles maintain the same shape, even if their sizes differ.
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Simplify this solution Mind Expander
For two triangles to be similar, they must satisfy two key conditions: the corresponding angles must be congruent, and the lengths of their corresponding sides must be in proportion. This means if you were to resize one triangle while keeping its angles the same, the smaller triangle would be like a mini version of the larger one! In real-world applications, understanding triangle similarity can be super helpful in fields like architecture or engineering. If you want to design a building model, for example, using similar triangles allows you to create accurate scale representations that maintain true proportions, ensuring your final structure aligns perfectly with your original vision.
