Question

Consider right triangles and . two right-angle triangles twx and tuv are connected at point t by 90 degrees. the xw and uv are congruent. the tx and tv are congruent. triangle is triangle . since triangle onto triangle using rigid motions, the triangles .

Answer 1

Triangle TXW and TUV are congruent triangles as they are connected by a 90 degree angle at point T and their sides are equal in length.

Step-by-step explanation:

Two right-angle triangles TXW and TUV are considered in the given scenario, which are connected at point T by 90 degrees. The XW and UV sides are congruent, i.e. of the same length, and the TX and TV sides are also congruent, i.e. of the same length. This means that the triangles TXW and TUV are congruent.

Congruence of triangles is a concept of geometry which states that two triangles are congruent when they have the same three sides and three angles. This means that the three sides of both the triangles have to be equal in length and the three angles of both the triangles have to be equal. In the given scenario, both the triangles are right-angle triangles, which means that the angles are 90 degrees in both cases.

The sides XW and UV are equal in length, and the sides TX and TV are also equal in length. This means that all the three sides are equal in both triangles, and the angles are equal in both triangles, i.e. 90 degrees. Therefore, it can be concluded that the two right-angle triangles TXW and TUV are congruent.