Question

If AB = AD, angle x = angle w, angle y = angle z. Then prove that AP= AQ

Answer 1

IT is given that 
<X =<W
and
<y =<Z
This gives
<X +<W=<y +<Z
<BAR=<DAR......................(1)

in triangle ADR and  ABR
AD=AB  [given]
DAR=BAR [eq.1]
AR = AR [common]
thus prooved these triangles are congruent[ASA]

<2=<1[CPCT]...................(2)

in triangle AQR and APR

<z=<y [given]
<2=<1 [eq.2]
AR=AR [comon]

thus prooved these two are congruent

therefore AQ =AP [CPCT]

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