Question

In the adjoining figure, angle BCD= angle ADC angle BCA = angle ADB. Prove that:
(i) ∆ACD congruent to ∆BDC
(ii) BC = AD
(iii) Angle A= Angle B.
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Answer 1

Step-by-step explanation:

We have ∠1=∠2 and ∠3=∠4

⇒∠1+∠3=∠2+∠4

⇒∠ACD=∠BDC.

Thus in triangles ACD and BDC, we have,

∠ADC=∠BCD   (given);

  CD  =   CD     (common);

∠ACD=∠BDC   (proved).

By ASA condition △ACD≅△BDC. Therefore