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11. ABC is an isoscales triangle in which AB=AC Show that <8=<C​

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Maths

The Triangle and Its Properties

Isosceles and Equilateral Triangles

ABC is an isosceles triangl...

MATHS

ABC is an isosceles triangle in which AB=AC. P is any point in the interior of ΔABC such that ∠ABP=∠ACP. Prove that

a) BP=CP

b) AP bisects ∠BAC

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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