IN A TRIANGLE ABC ANGLE ABC=90 DEGREES, AND P IS A POINT ON AC SUCH THAT ANGLE PBC =ANBLE PCB. SHOW THAT PA=PB

Asked by BHAVANA BHAT | 7th Jun, 2014, 10:36: PM

Expert Answer:

Given: ABC is a right angled triangle.

angleABC=90degree

anglePBC=anglePCB=a

To prove: PA=PB

In triangle ABC,

angleABC=90 andangle ACB=a

The sum of all angles of a triangle is 180degree.

angle ABC+angleACB+angleBAC=180degree

→90degree+a+angleBAC=180degree

angleBAC=180degree-90degree-a

angleBAC=90degree-a …(i)

angleABP=angleABC-anglePBC

angleABP=90degree-a …(ii)

angleBAC=angleABP … from (i) and (ii)

In a triangle sides opposite to equal angles are equal.

→ PA = PB

Answered by Anuja Salunke | 9th Jun, 2014, 10:04: AM

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