SOLUTION: Hello Geometry tutor, Please help me with my problem number 1. Given: ZM is perpendicular to XY, angle XZM is congruent to angle YZM. Prove: triangle XZY is isosceles. Thank

Question 377366: Hello Geometry tutor, Please help me with my problem number 1.
Given: ZM is perpendicular to XY, angle XZM is congruent to angle YZM.
Prove: triangle XZY is isosceles.
Thank you very much!
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Let the point of intersection of XY and ZM be B. Then from the given, Angle XBZ and Angle YBZ are right angles and supplementary. Hence triangle ZBX and triangle ZBY are right triangles. By the HA Theorem for right triangles, triangle ZBX and triangle ZBY are congruent, and so ZX is congruent to ZY. Hence triangle YZX is an isosceles triangle.
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