Question

in given fig side bc of triangle abc is produced to d if angle abc and anglw acd meet at e then prove that angle bec equal to one and half of angle bax

Answer 1

here is your answer

Answer 2

Step 1: Given Data:

AE bisects ∠ABC

CE bisects∠ACD  

To Prove: ∠BEC=1/2∠BAC  

Step 2: In ∠ABC

∠BAC + ∠ABC =1/2∠ACD

Therefore ½ ∠BAC +1/2 ∠ABC =1/2 ∠ACD

Therefore ½ ∠BAC +∠EBC=∠ECD ………………(1)

STEP 3: In ∠BEC

∠EBC+∠BEC=∠ECD………………….(2)

From (1) to (2) we get

STEP 4: ½ ∠BAC + ∠EBC = ∠EBC + ∠BEC

STEP 5: Therefore angle BEC=1/2 BAC

HENCE IT IS PROVED