Question

Prove that , In an Isosceles Triangle , If all angles are 3 angles are 60 ° , it is an equilateral Triangle .


I can prove it by trigonometry , but i have to prove it by congruence criterion​

Answer 1

Answer:

Step-by-step explanation:

CONSTRUCTION STEPS:

Sides BA and CA have been produced such that BA = AD and CA = AE.

To prove: DE ∥ BC

Consider △ BAC and △DAE,

BA = AD and CA= AE (Given)

∠BAC = ∠DAE (vertically opposite angles)

By SAS congruence criterion, we have

△ BAC ≃ △ DAE

We know, corresponding parts of congruent triangles are equal

So, BC = DE and ∠DEA = ∠BCA, ∠EDA = ∠CBA

Now, DE and BC are two lines intersected by a transversal DB s.t.

∠DEA=∠BCA (alternate angles are equal)

Therefore, DE ∥ BC. Proved.

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ADDITIONAL INFORMATION ❤

What is an isosceles triangle?

An isosceles triangle therefore has both two equal sides and two equal angles. The name derives from the Greek iso (same) and skelos (leg). ... An equilateral triangle is therefore a special case of an isosceles triangle having not just two, but all three sides and angles equal.

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Hope it helps you ❤

Answer 2

Answer:

Sides BA and CA have been produced such that BA = AD and CA = AE.

To prove: DE ∥ BC

Consider △ BAC and △DAE,

BA = AD and CA= AE (Given)

∠BAC = ∠DAE (vertically opposite angles)

By SAS congruence criterion, we have

△ BAC ≃ △ DAE

We know, corresponding parts of congruent triangles are equal

So, BC = DE and ∠DEA = ∠BCA, ∠EDA = ∠CBA

Now, DE and BC are two lines intersected by a transversal DB s.t.

∠DEA=∠BCA (alternate angles are equal)

Therefore, DE ∥ BC. Proved.