Question

In quadrilateral ABCD, AB = AD, and AC bisects A. D Show that ∆ABC  ADC. What can you say about BC and CD.

Answer 1

Answer:

Here is your answer:

Step-by-step explanation:

As we know that AB = AD and a bisector of angle A is AC.

So we have to prove that ABD is congruent with ACD.

AC is a bisector of A, then:

⇒ ∠DAC = ∠BAC

In ΔADC and ΔABC, we know that AD=AB and ∠DAC=∠BAC, hence:

⇒ AC = AC

By SAS, if two triangles have two equal sides or congruent sides, and an equal angle formed by these sides, then both triangles are congruent.

Hence, ΔABD ≅ ΔACD.

Answer 2

Answer:

Comparing ∆ABC and ∆ADC

1. AB=AD[given]
2. angle CAB=angle CAD[AC bisects A]
3. AC is a common side

so,we can say that ∆ABC[]∆ADC[as per S-A-S rule] {Proved}

So,BC=CD[as they are similar arms of uniform triangle]

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