Question

abcd is a quadrilacteral in which ab=bc and ad=cd show that bd bisects both the angles abc and adc

Answer 1

According to the question,

In ΔABC and ΔCBD,

We have

AB = BC

AD = CD

BD = BD [Common side]

ΔABC ≅ ΔCBD [By SSS congruence rule]

⇒ ∠1 = ∠2 [CPCT]

And ∠3 = ∠4

Hence, BD bisects both ∠ABC and ∠ADC.

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