Question

Identifying a Statement That Is Not True
Triangle Q S R. Angle Q is 98 degrees and angle R is 37.6 degrees. Triangle T U V. Angle U is 98 degrees and angle V is 37.6 degrees.

Which statement is not true about these triangles?
∠Q ≅ ∠T based on the third angle theorem.
∠S corresponds to ∠V.
∆QRS ~ ∆TVU based on the angle-angle criterion.
∆RQS ~ ∆VTU based on the angle-angle criterion

Answer 1

"∠Q ≅ ∠T based on the third angle theorem." is not true.

Reason: Q = 98°, R = 37.6° so S = 180 − 98 − 37.6 = 44.4°. In the other triangle U = 98°, V = 37.6° so T = 44.4°. So Q corresponds to U (both 98°), R corresponds to V (both 37.6°), and S corresponds to T (both 44.4°). Q (98°) is not congruent to T (44.4°), so the first statement is false.