ABC is an isosceles triangie with AB=AC,P and Q are points on AB and AC respectively such that AP=AQ
i) Is Triangle ABQ Congruent Triangle ACP
ii) Is Triangle BPC CongruentTriangle CQB ?
Give reasons in support of your answer
ΔABC is an isosceles triangle with AB = AC. P and Q are point on AB and AC respectively such that AP = AQ.
In ΔABC,
AB = AC (Given)
∴ ∠C = ∠B (Equal sides have equal angles opposite to them)
AB = AC (Given)
AP = AQ (Given)
∴ AB – AP = AC – AQ
⇒ BP = CQ
In ΔABQ and ΔACP,
AQ = AP (Given)
∠A = ∠A (Common)
AB = AC (Given)
∴ ΔABQ ΔACP (SAS congruence criterion)
In ΔBPC and ΔCQB,
BP = CQ (Proved)
∠B = ∠C (Proved)
BC = BC (Common)
∴ ΔBPC ΔCQB (SAS congruence criterion)