Question

in a triangle abc, ab=ac, ab is produced to d such that bd=bc. prove that angle acd= 3 angle adc.

Answer 1

This is your answer. Hope its helpful to u.

Answer 2

Answer:

Proved.

Step-by-step explanation:

Given:- In a triangle ABC, AB = AC and when AB is produced to D, BD = BC

To Prove:- ∠ACD = 3 ∠ADC

Solution:-

Given In triangle ABC, AB = AC.

Therefore, ∠ABC = ∠ACB  ------- ( 1 )

In triangle BDC, BD = BC

Therefore, ∠BDC = ∠BCD ----- ( 2 )

Ext. ∠ABC = ∠BCD + ∠BDC

∠ABC = 2∠BDC  ( from (2) )

⇒ ∠ACB = 2∠BDC    ( from (1) )

⇒ ∠ACB + ∠BCD = 2∠BDC + ∠BDC    ( from ( 2 ) )

⇒ ∠ACB + ∠BCD = 3∠BDC  

⇒ ∠ACD = 3∠BDC

⇒ ∠ACD = 3∠ADC

Hence Proved.

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