Question

1. given two triangles with two pairs of corresponding angles congruent, which of the following can you conclude? a. the triangles are similar. b. the triangles are congruent. c. the triangles are scalene. d. the triangles are isosceles. 10. what is the unique aspect of the sas method when constructing triangles? a. the method determines the largest side. b. the two sides must be equal in length. c. the included angle defines the shape of the triangle. d. the method requires all three angles. 11. which term describes triangles that have the same shape but different sizes? a. similar b. equivalent c. congruent d. identical

Explanation:

• For question 9, the AA (angle - angle) similarity criterion states that if two pairs of corresponding angles of two triangles are congruent, the triangles are similar. Congruent triangles require more than just two - angle congruence. Knowing only angle congruence doesn't determine if the triangles are scalene or isosceles.
• For question 10, in the SAS (side - angle - side) method of triangle construction, the included angle between the two given sides defines the shape of the triangle. It doesn't determine the largest side, the two sides don't have to be equal, and it doesn't require all three angles.
• For question 11, similar triangles have the same shape (corresponding angles are equal) but different sizes. Equivalent is not the correct term in this context, congruent triangles have the same shape and size, and identical means exactly the same in all respects including size.

Answer:

1. a. The triangles are similar.
2. c. The included angle defines the shape of the triangle.
3. a. Similar