Question

In triangle ABC AB equals to BC and in triangle ACD AD equals to CD prove that angle b a d equals to angle BCD

Answer 1

Answer:

Step-by-step explanation:

AB=BC ;given

AD=CD;given

Therefore, <DAC=<DCA; base angles of an isosceles triangle are equal

similarly, <BAC=<BCA

Therefore, BAC+DAC=BCA+DCA

Thus, we can tell that BAD =BCD

Hence proved

Answer 2

Answer with Step-by-step explanation:

In triangle ABC

AB=BC

Angle BAC=Angle BCA....(1)

Angle made by two equal sides are equal

In triangle ACD

AD=CD

Angle DAC=Angle DCA....(2)

Angle made by two equal sides are equal

Adding equation(1) and equation(2)

Then, we get

$\angle BAC+\angle DAC=\angle BCA+\angle DCA$

$\angle BAD=\angle BCD$

Hence, proved.

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