In the given triangle ABC, AB> AC and AD is the bisector of angle BAC then which of the following option is correct?
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∠ABD + ∠BAD < 90° is Correct if AB > AC & AD is bisector of angle BAC
Step-by-step explanation:
In the given triangle ABC, AB> AC
=> ∠ACB > ∠ ABC
AD is the bisector of angle BAC
=> ∠ BAD = ∠ CAD = x
∠ADB = ∠CAD + ∠ACD = x + ∠ACD = x + ∠ACB
∠ADC = ∠BAD + ∠ABD = x + ∠ABD = x + ∠ABC
now ∠ACB > ∠ ABC
=> ∠ADB > ∠ADC
∠ADB + ∠ADC = 180° ( straight line)
∠ADB > ∠ADC
=> ∠ADB > 90°
& ∠ADC < 90°
∠ADB = ∠DAC + ∠BCA > 90°
∠ADC = ∠ABD + ∠BAD < 90°
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