Question

In an isosceles triangle ABC, if AB = AC and AP perpendicular to BC, then prove BP = PC (using congruence of triangles) ?

Answer 1

here is your proof , see the above picture you will definitely understand

Answer 2

GIVEN: AN ISOSCELES TRIANGLE ABC
AB=AC
AP IS PERPENDICULER
TO PROVE: BP = PC
PROOF: IN ∆ABP AND ∆ ACP
AB= AC (GIVEN)
ANGLE APB= ANGLE APC = 90°
ANGLE ABP=ACP (in an isosceles triangle the angles opposite to the equal sides are also equal)
therefore, ∆ABP=~∆ACP
BP= PC (BY CPCT)