Question

Determine whether one figure is a dilation of the other. Complete the justification of your answer.Triangle XYZ has angles measuring 53° and 23º. Triangle X'Y'Z' has angles measuring 23°and 90°.Triangle X'Y'Z' is not a dilation of Triangle XYZ. The ratios of the lengths of the correspondingsides are equal because the triangles havethree pairs of congruent angles.havedo not have

Answer 1

If one triangle is the dilation of the other triangle, then they are similar

The addition of the angles in a triangle is equal to 180°

Triangle XYZ has angles measuring 53° and 23º, then the third angle measure:

53° + 23° + x = 180°

x = 180° - 53° - 23°

x = 104

AA similarity postulate states that If two angles in one triangle are congruent to two angles in another triangle, the two triangles are similar

In this case, the two triangles have only one angle in common, then the AA postulate is not satisfied, and the triangles are not similar nor dilated.

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