Question

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

Explanation:

Step1: Find base angles of △QRS

△QRS is isosceles with QR=QS. Let base angles be $x$.
$$x + x + 72^\circ = 180^\circ$$
$$2x = 180^\circ - 72^\circ = 108^\circ$$
$$x = 54^\circ$$

Step2: Find ∠T in △TUV

△TUV is isosceles with UT=VT. Let ∠T=∠U=y.
$$y + y + 56^\circ = 180^\circ$$
$$2y = 180^\circ - 56^\circ = 124^\circ$$
$$y = 62^\circ$$

Step3: Compare triangle angle sets

△QRS angles: $72^\circ, 54^\circ, 54^\circ$
△TUV angles: $62^\circ, 62^\circ, 56^\circ$
No matching angle pairs, so triangles are not similar.

Answer:

△QRS is not similar to △TUV.