Question

△qsu and △rst are shown below. which statement is true? △qsu is similar to △rst. △qsu is not similar to △rst. there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Calculate ∠Q in △QSU

First, find the missing angle in △RST:
$\angle T = 180^\circ - 50^\circ - 88^\circ = 42^\circ$
Since $\angle U = 40^\circ$, if △QSU ~ △RST, corresponding angles must match. Now calculate $\angle Q$:
$\angle Q = 180^\circ - \angle U - \angle S$
We know $\angle S$ (∠QSU) is equal to ∠RST = $88^\circ$ (common angle), so:
$\angle Q = 180^\circ - 40^\circ - 88^\circ = 52^\circ$

Step2: Compare triangle angles

Angles of △QSU: $40^\circ, 52^\circ, 88^\circ$
Angles of △RST: $50^\circ, 42^\circ, 88^\circ$
No set of corresponding angles are equal.

Answer:

△QSU is not similar to △RST.