Question

ABC is an isosceles triangle with AB=AC. Draw AP perpendicular BC to show that angle B=angle C

Answer 1

Hello mate ^_^

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Solution:

In △ABP and △ACP

AB=AC        (Given)

∠APB=∠APC          (Each equal to 90°)

AP=AP        (Common)

Therefore, by RHS congruence rule, △ABP≅△ACP

Hence, ∠B=∠C            (Corresponding parts of congruent triangles are equal)

hope, this will help you.

Thank you______❤

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Answer 2

Answer:

given : ABC is an isosceles triangle with AB=AC.  

To Prove : ∠B=∠C  

Construction: Draw AP⊥BC.  

Proof: In ΔABC,AP⊥BC and AB=BC.  

∴ In ΔABP and ΔACP

∠APB=∠APC=90  (∵AP⊥BC)  

Hypotenuse AB = Hypotenuse AC  

AP is common.  

As per RHS Postulate,  

ΔABP≅ΔACP  

∴ ∠ABP=∠ACP  

∴  ∠ABC=∠ACB  

∴ ∠B=∠C.