Question

given $\frac{tw}{uv}=\frac{wy}{vx}$ & $\angle w\cong\angle v$. complete the proof that $\triangle twy\sim\triangle uvx$.
answer
given the information above, we can prove $\triangle twy\sim\triangle uvx$ by

Explanation:

Step1: Recall the SAS (Side - Angle - Side) similarity criterion

Two triangles are similar if the ratio of two pairs of corresponding sides is equal and the included angles are congruent.
In \(\triangle TWY\) and \(\triangle UVX\), we are given \(\frac{TW}{UV}=\frac{WY}{VX}\) (ratio of two pairs of corresponding sides) and \(\angle W\cong\angle V\) (the included angles).

Answer:

By the SAS (Side - Angle - Side) similarity criterion, \(\triangle TWY\sim\triangle UVX\)