Question

In the following figure, AB = AD and ∠BAC = ∠DAC. Then 

1. ∆ ______ ≅ ∆ABC.
2. BC = ______.
3. ∠BCA = ______.
4. Line segment AC bisects ______ and ______.

Answer 1

1. ∆ADC ≅ ∆ABC
2. BC = DC
3. ∠BCA = ∠DCA
4. Line segment AC bisects ∠BAD and ∠BCD. 

Explanation:

In ∆ABC and ∆ADC,

AC = AC   ...[Common]

∠BAC = ∠DAC  ...[Given]

AB = AD  ...[Given]

∴ ∆ABC ≅ ∆ADC  ...[SAS criterion]

∴ BC = DC  ...[By C.P.C.T.]

And ∠BCA = ∠DCA  ...[By C.P.C.T.]