Question

In the figure triangle ABD and triangle BCD are isosceles triangle on the same base BD . Prove that angle ABC =angle ADC​

Answer 1

Answer:

Step-by-step explanation:

Angles opp to equal sides of a triangle are equal. Apply this in both triangles.

ABD=ADB

CBD=CDB, Add both.

here, two concepts are used angle opp to equal sides.., Sum to two equal values in diff forms then also gives same value in diff form.

Answer 2

Given:

• ΔABD and ΔBCD are isosceles triangles.
• They have the same base BD.

To Find:

• To prove that, ∠ABC = ∠ADC

Solution:

• In an isosceles ΔABC, AB = AD
• Therefore, ∠ABD = ∠ADB → (1) (∵ The angles opposite to equal sides of a triangle are equal)
• Since, ΔCBD is an isosceles, CB = CD

• Therefore, ∠CBD = ∠CDB → (2) (∵ The angles opposite to equal sides of a triangle are equal)

• Adding equation (1) and (2) we get,
• ∠ABD + ∠CBD = ∠ADB + ∠CDB
• ∠ABC = ∠ADC

Hence Proved.

∠ABC = ∠ADC.