Question

Triangle XYZ is isosceles. The measure of the vertex angle, Y, is twice the measure of a base angle.

What is true about triangle XYZ? Select three options.

Angle Y is a right angle.
The measure of angle Z is 45°.
The measure of angle X is 36°.
The measure of the vertex angle is 72°.
The perpendicular bisector of Line segment X Z creates two smaller isosceles triangles.

Answer 1

True:
- Angle Y is a right angle. (Let each base angle = b. Then b + b + 2b = 180 ⇒ 4b = 180 ⇒ b = 45°, so Y = 2b = 90°.)
- The measure of angle Z is 45°. (Z is a base angle.)
- The perpendicular bisector of segment XZ creates two smaller isosceles triangles. (In this isosceles 45°-45°-90° triangle the perpendicular from the vertex Y to the base XZ bisects XZ and produces two congruent right isosceles triangles.)

False:
- The measure of angle X is 36°. (X = 45°.)
- The measure of the vertex angle is 72°. (Vertex Y = 90°.)