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Question
In the following figure, AD ⊥ BC and AD is the bisector of angle BAC. Then, ∆ABD ≅ ∆ACD by RHS.
Options
True
False
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Solution
This statement is False.
Explanation:
In ∆ABD and ∆ACD,
AD = AD ...[Common]
∠BAD = ∠CAD ...[∵ AD is the bisector of ∠BAC]
∠ADB = ∠ADC ...[Each 90°, ∵ AD ⊥ BC]
∴ ∆ABD ≅ ∆ACD ...[By ASA criterion]
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