Question

In the figure, D and E are points
on the base BC of A ABC such
that BD = CE. Prove that
NABE ARA
B
DE
AL BD
ДАВЕ - SACD.​

Answer 1

Answer:

Step-by-step explanation:

Given: D and E are points on the base BC of a ∆ABC such that AD = AE and ∠BAD = ∠CAE.

To Prove: AB = AC

Proof: In ∆ADE,

∵ AD = AE    | Given

∴ ∠ADE = ∠AED    ...(1)

| Angles opposite to equal sides of a triangle are equal

In ∆ABD,

Ext. ∠ADE = ∠BAD + ∠ABD ...(2)

| An exterior angle of a triangle is equal to the sum of its two interior opposite angles

In ∆AEC,

Ext. ∠AED = ∠CAE + ∠ACE .. .(3)

| An exterior angle of a triangle is equal to the sum of its two interior opposite angles

From (1), (2) and (3),

∠BAD + ∠ABD = ∠CAE + ∠ACE

⇒ ∠ABD = ∠ACE

| ∵ ∠BAD = ∠CAE (Given)

⇒ ∠ABC = ∠ACB

∴ AB = AC

| Sides opposite to equal angles of a triangle are equal

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