Geometry Questions

Question

Triangle XYZ is taken by a dilation with center Y and scale factor 5/2 to Triangle X’Y’Z’. The measure of angle YXZ is 83 degrees and the measure of angle YZX is 22 degrees.

Task 1: a) What is the measure of angle Y’Z’X’? Explain your reasoning.

Type your answer here…

Task 2: b) What is the measure of angle X’Y’Z’? Explain your reasoning.

Answer 1

Angle Y'Z'X' = YZX = 22 degrees ( in triangle dilation size of angles does not change. only sides length change.).

Task 2 -b) In triangle XYZ

angle XYZ = 180 - 83 -22 = 75 degrees(sum of angles of triangle . two angles are given so third angle is 75 degrees)

therefore X'Y'Z' =XYZ = 75 degrees.. ( same reason as in first task in dilation angle size does not change.)

Answer 2

Dilation produces a similar figure to the original, so triangle X'Y'Z' is similar to triangle XYZ. In similar triangles, the side lengths are related by the scale factor - the sides in X'Y'Z' are 5/2 longer than in XYZ - but the angles remain the same. So:

m∠Y'Z'X' = m∠YZX

and

m∠X'Y'Z' = m∠XYZ

So just figure out what the angles are in triangle XYZ; the corresponding angles in X'Y'Z' are the same. Remember that the sum of the three angles in a triangle is 180º.