Question

In the given figure AD = AE, BD = EC, prove that ABC is an isosceles triangle.

Answer 1

I dont know the picture but i hope my guess is right


In triangle ADE ,

AD = AE [given]

⇒ ∠AED = ∠ADE [angles opposite to equal sides are equal]

⇒ 180 - ∠AED = 180 - ∠ADE

⇒∠AEC = ∠ADB ............(1)

in Δ ABD and Δ ACE

AD = AE [ given ]

∠ADB = ∠AEC [ using (1) ]

BD = CE [ GIVEN ]

Δ ABD is congruent to Δ ACE [ SAS ]

⇒ AB = AC [ CPCT ]

Answer 2

Answer:

Given,

AD=AE  where, D and E are points on BC,

Such that BD = EC,

To prove :

AB = AC,

Proof :

∵ AD=AE

⇒ ∠ADE = ∠AED

⇒ 180° -  ∠ADE =  180° -  ∠AED

⇒ ∠ADB = ∠AEC,

BD = EC ( given )

By SAS postulate of congruence,

Δ ABD ≅ Δ ACE

By CPCT,

AB = AC

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