Question

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

Triangle XYZ has angles measuring 54º and 25º. Triangle X'Y'Z' has angles measuring 25°and 88°.

Triangle X'Y'Z (is/is not) a dilation of Triangle XYZ. The ratio 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

not a dilation

Explanation:

When one triangle is a dilation of another, they are similar. That is, their corresponding angles are congruent, and their corresponding sides are proportional.

In ∆XYZ, the angle not given is 180° -54° -25° = 101°, so its three angles are ...

{25°, 54°, 101°}

In ∆X'Y'Z', the angle not given is 180° -25° -88° = 67°, so its three angles are ...

{25°, 67°, 88°}

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