ICSE Class 9 Answered
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 | 07 Jun, 2014, 10:36: PM
Expert Answer
Given: ABC is a right angled triangle.
ABC=90
PBC=PCB=a
To prove: PA=PB
In ABC,
ABC=90 and ACB=a
The sum of all angles of a triangle is 180.
→ ABC+ACB+BAC=180
→90+a+BAC=180
→BAC=180-90-a
→BAC=90-a …(i)
ABP=ABC-PBC
ABP=90-a …(ii)
→BAC=ABP … from (i) and (ii)
In a triangle sides opposite to equal angles are equal.
→ PA = PB
Answered by Anuja Salunke | 09 Jun, 2014, 10:04: AM
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