Question

ABC is an isosceles triangle in which AB= AC if p and Q are the mid points of AB and AC resepctively , show that BQ=CP

Answer 1

Solution is in the pic

Answer 2

Hey there!

$Given,\\ In \ \triangle ABC,\\AB = AC\\\text{P and Q are mid points of AB and AC.}\\So,AP = BP\\ And, AQ = QC\\\\Now, \text{In }\triangle BCP \ and \ \triangle CBQ,\\ \angle B = \angle C~~~~~~~~~(opp. \ \angle s \ of \ isosceles \ \triangle \ are \ equal )\\BC = BC~~~~~~~~~(common)\\PB = QC~~~~~~~~(P \ and \ Q \ are\ mid \ points)\\\triangle BCP \cong \triangle CBQ~~~~~~~~~~~~(By \ SAS \ axiom) \\BQ = CP~~~~~~~~~(C.P.C.T.C)$

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