in quadrilateral ABCD AC bisects angle C and BC equals to CD prove that AB = AC.
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Quadrilateral ABCD.
AC bisects angle C. BC = CD.
To prove AB = AD. Not AB = AC. There is a mistake in the given question.
Compare ΔACB, and ΔACD:
∠ACB = ∠ACD (given AC bisects)
AC = AC. and given CB = CD
So as per SAS law both triangles are congruent.
So AD = AB.
=> In ΔABD, So ∠ABD = ∠ADB.
In ΔBCD, BC = BD so ∠CBD = ∠CDB
Hence ∠ABC = ∠ADC.
Using the above equalities, we can say the AC bisects ∠A also.
AC bisects angle C. BC = CD.
To prove AB = AD. Not AB = AC. There is a mistake in the given question.
Compare ΔACB, and ΔACD:
∠ACB = ∠ACD (given AC bisects)
AC = AC. and given CB = CD
So as per SAS law both triangles are congruent.
So AD = AB.
=> In ΔABD, So ∠ABD = ∠ADB.
In ΔBCD, BC = BD so ∠CBD = ∠CDB
Hence ∠ABC = ∠ADC.
Using the above equalities, we can say the AC bisects ∠A also.
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