Question

refer to the figure shown. which of the following statements is true?

a. △tuv≅△wxv by asa
b. △tuv≅△vxw by sas
c. △tuv≅△wxv by sas
d. △tuv≅△wxv by sss
tv≅wv uv≅xv

Explanation:

Step1: Recall congruence postulates

SAS (Side - Angle - Side) postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Step2: Analyze given information

We are given that $\overline{TV}\cong\overline{WV}$ and $\overline{UV}\cong\overline{XV}$. The included angle for these pairs of sides in $\triangle TUV$ and $\triangle WXV$ is the vertical - angle pair $\angle TVU$ and $\angle WVX$ which are congruent (vertical angles are congruent).

Step3: Determine congruence

By the SAS postulate, $\triangle TUV\cong\triangle WXV$.

Answer:

C. $\triangle TUV\cong\triangle WXV$ by SAS