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Question
In the following figure, AB = AD and ∠BAC = ∠DAC. Then
- ∆ ______ ≅ ∆ABC.
- BC = ______.
- ∠BCA = ______.
- Line segment AC bisects ______ and ______.
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Solution
- ∆ADC ≅ ∆ABC
- BC = DC
- ∠BCA = ∠DCA
- 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.]
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