Question

ABC is a isoscles triangle in which AB parallel AC . AD bisect exterior angle and CD parallel AB ( see fig 8.4 )show that. (1) angle DAC = angle BCA (2) ABCD IS A PARALLELOGEAM

Answer 1

∠ACB+ ∠ABC= ∠CAP ( exterior angle is equal to sum of opp. interior angles)
so, ∠CAP= 2 ∠ACB =2ABC
so,
∠CAP= 2∠CAD= 2∠DAP
so, ∠ACB=∠CAD 
but they are alt interior angles
so, AD parallel to DC

hence ABCD is a parallelogram