Question

Abcd is a parallelogram in which angle a=60°.If the bisector of angle a and angle b meet at p,proove that ad=dp,pc=bc and dc=2ad

Answer 1

poa =30 (ap is the bisector of angle A )
an angle pBA equals to 60 (PB is the bisector of Angle B )
so in triangle pab
apb = 90
in in triangle ADp

dap+dpa+ADp=180
30+120+dpa=180
dpa=30
dap=dpa
so
ad = dp
in triangle pcb
pcb+cbp+cpb= 180
60+60+cpb=180
cpb=60
all angles equal


triangle PCB is a equilateral triangle
pc=bc=pb
ad=dp,bc=pc
add both equation ad+bc=dc
2ad=dc