Question

in triangle abc ad bisect a angle c graeter than b prove adb greater adc​

Answer 1

Answer:

Given : m∠C > m∠B and AD bisects ∠A

To Prove : m∠ADB > m∠ABC

Proof : Since m∠C > m∠B

⇒ m∠ACB > m∠ABC

⇒ m∠ACB + m∠CAD > m∠ABC + m∠BAD .....(1)

(AD bisects ∠A ⇒m∠CAD = m∠BAD )

In ΔABD,

m∠ABC + m∠BAD + m∠ADB = 180°

Therefore, m∠ABC + m∠BAD = 180° – ∠ADB ....(2)

In ΔACD,

m∠ACD + m∠CAD + m∠ADC = 180°

Therefore, m∠ACB + m∠CAD = 180° – m∠ADC ....(3)

From (1), (2) and (3), we get

180° – m∠ADC > 180° – m∠ADB

⇒ m∠ADB – m∠ADC > 180° – 180°

⇒ m∠ADB – m∠ADC > 0

⇒ m∠ADB > m∠ADC

Hence proved.

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