Question

Identifying and naming congruent trianglesFor each figure below, determine (by using the markings) if there is a pair of congruent triangles. If there is, name the congruence and give the property justifying the congruence.Note that the pairs of triangles are drawn as congruent, but you should not rely on how they are drawn in determining your answers.If necessary, you may learn what the markings on a figure indicate.

Answer 1

In the first pair of triangles, we can see that the two triangles share 2 angles and 1 side length, but, we don't have enough information about the corresponding sides and angles to assure congruency.

The answer to the first pair is: Not necessarily congruent.

In the second pair, we can see that again they share 2 angle measures and 1 side length. If we mirror the triangle XYZ, the angles and side length of the corresponding sides will match, and by ASA theorem, we can assure that:

The answer to the second pair is: Congruent

`\triangle UVW\cong\triangle XYZ`

By the angle-side-angle

In the third pair, if we rotate the triangle PQR by 180º, we can see that the two triangles share the lengths of two corresponding sides and an angle measure of corresponding angles. Thus,

The answer to the third pair is: Congruent

`\triangle MNO\cong\triangle PQR`

by the side-angle-side