Question

in right triangle δqrs, m∠s = 73°. in right triangle δtuv, m∠v = 73°. which similarity postulate or theorem proves that δqrs and δtuv are similar?
a. sas
b. aa
c. hl
d. sss

Explanation:

1. Recall similarity postulates and theorems:

• SAS (Side - Angle - Side) requires two pairs of proportional sides and the included angle equal. No information about sides is given here.
• AA (Angle - Angle) states that if two angles of one triangle are congruent to two angles of another triangle, the triangles are similar. In right - triangles $\triangle QRS$ and $\triangle TUV$, both are right - triangles (so one pair of right angles are equal) and $\angle S=\angle V = 73^{\circ}$, so two pairs of angles are equal.
• HL (Hypotenuse - Leg) is for congruence of right - triangles, not similarity, and requires information about the hypotenuse and a leg.
• SSS (Side - Side - Side) requires all three pairs of sides to be proportional. No side information is given.

Answer:

B. AA