Question

16. In AABC, AB = AC and AP = AQ. Prove that
CP = BQ.
А
B
P​

Answer 1

Step-by-step explanation:

In the adjoining figure P and Q are two points on equal sides AB and AC of an isosceles triangle ABC such that AP = AQ , prove that BQ = CP

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ANSWER

REF. Image.

Given AB=AC

and AP=AQ

Thus

AB-AP=AC-AQ

[BP=CA ] [from figure ]

now InΔBCP & ΔBCQ

BP = CQ

∠c=∠c [common]

and BC=BC [common]

∴ΔBCP≃ΔBCQ [SAS congruency]

now

[BQ=CP] [corresponding parts of congruent triangles]

solution