Question

logical reasoning decide whether enough information is given to prove that the triangles are congruent. if there is enough information, state the congruence postulate you would use. 12. △uvt, △wvt

Explanation:

Step1: Analyze the given information

We know that \( \angle TVU=\angle TVW = 90^{\circ}\) (right angles), \(WV = VU\) (marked as equal), and \(TV\) is a common side.

Step2: Apply the congruence postulate

For right - angled triangles, if the hypotenuse and one leg are equal, we can use the Hypotenuse - Leg (HL) congruence postulate. Here, in right triangles \(\triangle UVT\) and \(\triangle WVT\), \(TV\) is the leg, \(WT = UT\) (since \(WV = VU\) and \(TV\) is common, by Pythagoras \(WT^{2}=WV^{2}+TV^{2}\) and \(UT^{2}=VU^{2}+TV^{2}\)), and \(\angle TVU=\angle TVW\).

Answer:

Yes, enough information. The congruence postulate is the Hypotenuse - Leg (HL) postulate.