Question

In given figure AB=AC, BD=EC. prove that ∆ABE congruent to ∆ACD and AD=AE

Answer 1

Since, AB = AC
Angle B = Angle C

Also,
BD = EC
BD + DE = EC + DE
BE = CD

Now, in triangles ABE and ACD,
angle B = angle C
AB = AC
BE = CD

Therefore, by SAS criterion
ABE is congruent to ACD

Also,
AD = DE by cpct

Answer 2

Answer:

ΔABE ≅ ΔACD and AD = AE are proved.

Step-by-step explanation:

Given:-

In the figure, AB = AC, BD = EC.

To prove:-

ΔABE ≅ ΔACD and AD = AE.

Step 1 of 2

According to the question,

Since AB = AC.

⇒ ∠ACD = ∠ABE ___ (i) (Angles opposite to equal sides are equal)

Also,

BD = EC

BD + DE = EC + DE (Adding DE on both the sides)

BE = DC _____ (ii)

Now,

In ΔABE and ΔACD,

AB = AC (Given)

∠ABE = ∠ACD (From (i))

BE = DC (From (ii))

By SAS congruence rule,

ΔABE ≅ ΔACD

Step 2 of 2

Since ΔABE ≅ ΔACD.

Then by CPCT,

AD = AE.

Hence proved

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