Question

in a triangle if AB=AC.D is a point on AC amd E is a point on AB such that AD=DE=EC=BC. Prove that angle A =angle B =1:3

Answer 1

GIVEN:

AB = AC

AD = DE = EC = BC

TO PROVE:

<A : <B = 1:3

PROOF:

Since AD = DE

=> < A = < AED = x ( isosceles triangle)…….(1)

=> < CDE = x + x = 2x ( exterior angle = the sum of 2 opposite interior angles)

But, DE =CE ( given)

So, < CDE = < DCE = 2x

=> < BEC = 2x + x = 3x ( exterior angle of triangle ACE )

And CE = CB ( given)

=> < CEB = < CBE = 3x …………(2)

By (1) & (2)

< A / <B = x/3x = 1/3

<A : <B = 1 : 3

PROVEN: 

<A = <B = 1:3

HOPE IT HELPS.......................... PLZ MARK IT AS BRAINLIST

Answer 2

Answer: ang A: ang B=1:3

Step-by-step explanation:

TO PROVE : ang A: ang B=1:3

PROOF : ang A = ang AED = x ( isosceles triangle)…….(1)

=> ang CDE = x + x = 2x ( exterior angle = the sum of 2 opposite interior angles)

But, DE =CE ( given)

So, ang CDE = ang  DCE = 2x

=> ang BEC = 2x + x = 3x ( exterior angle of triangle ACE )

And CE = CB ( given)

=> ang CEB = ang CBE = 3x …………(2)

By (1) & (2)

ang A / ang B = x/3x = 1/3

<A : <B = 1 : 3

PROVEN: 

<A = <B = 1:3