Question

А 1. In the figure, AB = AC and point P is in the interior of triangle ABC such that PB = PC, then prove Angle ABP congruent of Angle ACP . standard 9 th
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Answer 1

Answer:

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