Question

in the figure ΔABC is isosceles with AB=AC ΔAPQ is also an isosceles triangle with AP = AQ also ∠BAC = ∠PAQ prove that (i) ∠BAP = ∠CAQ (ii) Δ's BAP and CAQ are congruent

Answer 1

Step-by-step explanation:

Given ABC is a trianlge in which AB=AC . P is any point in the interior of the triangle such that angle ABP=ACP

In ΔAPB and ΔAPC,

AB=AC[given]

∠ABP=∠ACP [given]

AP=AP[common]

ΔAPB≅ΔAPC[by SAS congruency criterion]

∴∠PAB=∠PAC [corresponding angles of congruent trianlges]

thus, BP=CP

And AP bisects ∠BAC