Question

1. what is the purpose of the sas similarity criterion? a. to identify supplementary angles b. to prove the similarity of two triangles c. to calculate the perimeter of triangles d. to determine congruence between triangles 11. given two triangles are congruent, what can be said about their corresponding angles? a. they are right angles b. they are supplementary c. they are equal d. they are complementary 12. which of the following ratios would not indicate sss similarity? a. 1/3, 2/6, 3/9 b. 4/5, 8/10, 12/15 c. 3/m, 7/n, 9/p d. 2/4, 3/6, 5/10

Explanation:

1. The SAS (Side - Angle - Side) similarity criterion is used to prove that two triangles are similar. If the ratios of two pairs of corresponding sides are equal and the included angles are congruent, the triangles are similar.
2. By the definition of congruent triangles, corresponding parts of congruent triangles are equal (CPCTC). So, if two triangles are congruent, their corresponding angles are equal.
3. For SSS (Side - Side - Side) similarity, the ratios of the corresponding sides of two triangles must be equal. In option a, the ratios $\frac{1}{3},\frac{2}{4},\frac{3}{5}$ are not equal since $\frac{1}{3}

eq\frac{2}{4}
eq\frac{3}{5}$.

Answer:

1. B. To prove the similarity of two triangles
2. C. They are equal
3. A. $\frac{1}{3},\frac{2}{4},\frac{3}{5}$