Question

In Fig., $$AB = AD$$ and $$\angle BAC = \angle DAC$$.
Then,
(i) $$\Delta$$ ______ $$\cong \Delta ABC$$
(ii) $$BC =$$ ______
(iii) $$\angle BCA =$$ ______
(iv) Line segment $$AC$$ bisects ______ and ______.

Answer 1

(i) In $$\triangle ABC$$ and $$\triangle ADC$$

$$AC = AC$$ [Common]

$$\angle BAC = \angle DAC$$ [Given]

$$AB = AD$$ [Given]

$$\therefore \triangle ABC = \triangle ADC$$ [by SAS criterion]

(ii) We have, $$\triangle ABC = \triangle ADC$$

$$\Rightarrow BC = DC$$ [by C.P.C.T.]

(iii) and, $$\angle BCA = \angle DCA$$ [by C.P.C.T.]

(iv) Given that $$\angle BAD=\angle BCD$$

Hence, Line segment $$AC$$ bisects $$\angle BAD$$ and $$\angle BCD$$