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In the adjoining figure, AB = AC, P and Q are points on BA and CA respectively such that AP=AQ. Prove that
(i) ∆APC ≌ ∆AQB
(ii) CP = BQ
(iii) ∠ACP = ∠ABQ.

Dear student, In triangle ADB and triangle BCA  AD=BC (GIVEN)  DB=CA (GIVEN)  angleDAB=angleABC (ANGLES OPPOSITE TO EQUAL SIDES ARE ALSO EQUAL)  SO,TRIANGLE ADB CONGRUENT TO TRIANGLE BCA (SAS)  SO,angle ADB=angleBCA (CPCT) ALSO, angle DAB =angleCBA (CPCT) Regards

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