Question

analyzing triangle
in the figure, (overline{wt}congoverline{vt}).
the congruency theorem can be used to prove that
(\triangle w) tu.

Explanation:

Step1: Recall congruency theorems

• SSS (Side - Side - Side): If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
• HL (Hypotenuse - Leg): Applies to right - angled triangles. If the hypotenuse and a leg of one right - angled triangle are equal to the hypotenuse and a leg of another right - angled triangle, the triangles are congruent.
• SAS (Side - Angle - Side): If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
• AAS (Angle - Angle - Side): If two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle, the triangles are congruent.

Step2: Analyze the given triangles

• We are given \(WT\cong VT\).
• Since \(\angle WTY\) and \(\angle VUY\) are right angles (\(\angle WTY=\angle VUY = 90^{\circ}\)), and \(\angle WYT=\angle VYU\) (vertically opposite angles).
• Also, \(WT\cong VT\) (given). So, we have two angles (\(\angle WTY=\angle VUY\) and \(\angle WYT=\angle VYU\)) and a non - included side (\(WT\cong VT\)) that are equal.

Answer:

AAS