Question

in the figure if AD is the bisector of angle A, Show that AC>CD​

Answer 1

Step-by-step explanation:

ANSWER

In ΔABC ,

AC>AB (given)

So,

∠B>∠C ............... (1) ( Angle opposite to the larger side is Larger )

In ΔABD,

∠1+∠B+∠ADB=180

∘

∠B=180

∘

−∠1−∠ADB .................... (2)

In ΔADC,

∠2+∠C+∠ADC=180

∘

∠C=180

∘

−∠2−∠ADC .................... (3)

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

180 ∘ −∠1−∠ADB>180 ∘

−∠2−∠ADC180 ∘

−∠1−∠ADB>180

∘

−∠1−∠ADC ( ∠1=∠2 )

−∠ADB>−∠ADC

⇒∠ADB<∠ADC