Question

In adjacent figure AB = AD, angleBAC = angleCAD. Prove that AC bisects angleBCD.
✨ Please answer briefly ✨ ​

Answer 1

Answer:

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