In adjacent figure AB = AD, angleBAC = angleCAD. Prove that AC bisects angleBCD.
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Here we've to prove
AC bisects BCD
therefore we've to prove that
angle ACD=ABD
For that we've to prove those triangles are congruent
that is
Consider
∆ACD & ∆ACB
AC=AC(common side)
AB=AD(given)
also
angleBAC = angleCAD (given)
or Angle A= Angle A
therefore by A.S.S congruent
∆ACD ≈ ∆ACB
And by corresponding parts of a congruent triangle (C.P.C.T)
angle ACD= angle ABD
therefore
AC is a bisector of BCD
hope it helps
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