Question

In triangle ABC, AB = AC. If P is a point on AB and Q is a point on AC such that AP =

AQ. Prove that:

∆ APC ≅ ∆ AQB

∆ BPC ≅ ∆ CQB​

Answer 1

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Answer 2

GIVEN - AB = AC

AP=AQ

TO PROOF  APC  = ABC

BPC = CQB

PROOF - AB = AC (GIVEN)

AP+PB=AQ+QC

AP-AQ+PB=QC

PB = QC

IN TRAINGLE APC = AQB

AP=AQ ( GIVEN )

<A=<A( COMMON )

AC = AB ( GIVEN )

APC = AQB ( BY SAS )

PC = QB ( BY P.C.T)

IN TRAINGLE BPC AND TRAINGLE CQB -

BP=CQ( PROVED ABOVE )

BC=BC ( COMMON)

PC = QB ( PROVED ABOVE )

HENCE TRAINGLE BPC = CQB (BY SSS)