Question

ABC is an isosceles triangle with AB = AC. Draw AP ⊥ BC to show that∠ B = ∠ C.​

Answer 1

Step-by-step explanation:

take a triangle ABC right angled at A. it is given AB=AC.

to prove,  

∠B=∠C

CONSTRUCTION : DRAW A PERPENDICULAR BISECTOR OF LINE BC TO A. THE POINT WHICH CUTE ON BC LINE BY PERPENDICULAR BISECTOR N, NAME IT AS D.

NOW, IN ΔABD AND ΔACD

∠ADB=∠ADC (90 DEGREES EACH)

AB=AC (GIVEN)

AD=AD (COMMON)

ΔABD≅ΔACD ( BY RHS CONGRUENT RULE)

∠B=∠C (BY CPCT)

HOPE THIS WILL HELP...........

Answer 2

in triangle APB and APC

AP = AP common in both

AB= AC given

angle APB = angle APC = 90

by congruency rule SAS

triangle APB = triangle APC

by corresponding part of congruent triangle

/B = /C

hence proved