Math, asked by Atharv7275, 10 months ago

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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Answered by amitnrw
11

∠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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