Question

1. consider the following triangles.

7b give the reason for your choice.
a. hl: two right triangles with hypotenuse and one leg are congruent.
b. aas: a pair of corresponding angles and a non-included side are congruent.
c. sas: a pair of corresponding sides and the included angle are congruent.
d. sss: all three corresponding sides are congruent.

Explanation:

First, calculate the third angle of each triangle to confirm all corresponding angles are congruent. For the first triangle: $180^\circ - 46^\circ - 99^\circ = 35^\circ$. For the second triangle: $180^\circ - 46^\circ - 99^\circ = 35^\circ$. The first triangle has a side of length 10 adjacent to the $46^\circ$ and $99^\circ$ angles, meaning this side is non-included relative to the $46^\circ$ and $35^\circ$ angles. The second triangle has a side of length 13 adjacent to the $46^\circ$ and $99^\circ$ angles, also non-included relative to the $46^\circ$ and $35^\circ$ angles. This matches the AAS congruence criterion, where two corresponding angles and a non-included corresponding side are congruent.

Answer:

B. AAS: A pair of corresponding angles and a non-included side are congruent.