Q.11. In the figure, AY perpendicular to ZY and BY perpendicular to XY such that AY = ZY and BY = XY. Prove that AB = ZX.

Solution :

Clearly ZYA=XYB=90° given ZYA+AYX=XYB+AYXZYX=AYB  ...1Consider AYB and ZYXAY=ZY givenBY=XY givenAYB=ZYXusing 1So, AYBZYX   SASAB=ZX   c.p.c.t

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in triangle ayb & zyx

​ay = zy(given)
by=yx(given)
angle zya+angle ayx = angle byx +angleayx (adding angle ayx to both the sides and zya &byx are 90 each)
so,
triangle ayb = congruent = triangle zyx
by cpct 
ab=zx

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