Question

Determine whether one figure is a dilation of the other. Complete the justification of your answer.

Triangle XYZ has angles measuring 59° and 22º. Triangle X'Y'Z' has angles measuring 22 and 90°.

Triangle X'Y'Z' (is/is not) a dilation of Triangle XYZ. The ratios of the lengths of the corresponding sides (are/are not) equal because the triangles (have/do not have) three pairs of congruent angles.​

Answer 1

Triangle X'Y'Z' is not a dilation of Triangle XYZ; do not have congruent angles

Explanation:

In order to determine if two triangles have three pairs of congruent angles, we need to be able to determine if there are at least two pairs of congruent angles. Here, we see both triangles have an angle measuring 22°, but that is not sufficient to tells us if a second angle pair is congruent. So, we figure all three angles in each triangle from the given information.

∆XYZ angles are 22°, 59°, 180-22-59 = 99°

∆X'Y'Z' angles are 22°, 90-22 = 68°, 90°

There are not three pairs of congruent angles in these triangles. Ratios of corresponding sides cannot be equal, and the triangles cannot be similar (dilations of each other).