Question

ABC is an issoceles triangle in which AB=AC,CP//AB and AP is the bisector of exterior angle CAD of triangle ABC. prove that
(1)anglePAC=angleBAC
(2)ABCP is a parallelogram

Answer 1

angleABC+angleACB=anglePAC +anglePAD { EXTERIOR ANGLE THEOREM}

PAC= PAD {GIVEN}

ABC = ACB {ANGLES OPPOSITE TO EQUAL SIDES ARE EQUAL}

2 × PAC = 2 × ACB

PAC=ACB

=> ap is parallel to to bc

similarly ab is parallel to cp


hence abcd is parallogram