Question

TIME REMAINING

43:25
Triangles X Y Z and X prime Y prime Z prime are shown.

ΔXYZ was reflected over a vertical line, then dilated by a scale factor of One-half, resulting in ΔX'Y'Z'. Which must be true of the two triangles? Select three options.

△XYZ ~ △X'Y'Z'
AngleXZY ≅ AngleY'Z'X'
YX ≅ Y'X'
XZ = 2X'Z'
mAngleYXZ = 2mAngleY'X'Z'

Answer 1

• △XYZ ~ △X'Y'Z'
• AngleXZY ≅ AngleY'Z'X'
• XZ = 2X'Z'

Explanation:

Reflection over any line is a rigid transformation that does not change angles or lengths. Dilation is a transformation that changes lengths by the same scale factor, but has no effect on angles. Dilated figures are similar to the original.

Application

When ΔXYZ is reflected over a vertical line, no lengths or angles are changed. When the reflected triangle is dilated by half, we get ...

Y'X' = (1/2)YX . . . . . . . makes option 3 false

X'Z' = (1/2)XZ . . . . . . . makes option 4 true

Since no angles are changed, we have ...

Angle XZY ≅ Angle Y'Z'X' (another name for angle X'Z'Y')

... makes option 2 true

Of course, the resulting triangle is similar to the original, so ...

△XYZ ~ △X'Y'Z' . . . . . option 1 is true