Chapter 4: Q28. (page 139)

Given: $∠ 4 ≅ ∠ 7; ∠ 1 ≅ ∠ 3$
Prove: $Δ ABC$ is isosceles.

Short Answer

Expert verified

It is proved that $Δ A B C$ is an isosceles triangle.

Step by step solution

– Description of step.

It is given that, $∠ 4 ≅ ∠ 7$ and the angle adjacent to congruent sides are congruent, that is, $∠ 5 ≅ ∠ 6$ .

– Converse of isosceles triangle theorem.

If two angles of triangle are congruent then the sides opposite to those angles are congruent.

As $∠ 5 ≅ ∠ 6$ . Therefore, by converse of isosceles triangle theorem, $\bar{A L} ≅ \bar{A M}$ .

– ASA postulate.

If two angles and included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

Here, $∠ 4 ≅ ∠ 7, \bar{A L} ≅ \bar{A M}$ and $∠ 1 ≅ ∠ 3$ , then by ASA postulate $Δ A B L ≅ Δ A C M$ .

– Description of step.

As $Δ A B L ≅ Δ A C M$ , therefore, by congruent parts of congruent triangles, $\bar{A B} ≅ \bar{A C}$ .

– Description of step.

As, $\bar{A B} ≅ \bar{A C}$ , then by definition of isosceles triangle, $Δ A B C$ is an isosceles triangle.

Hence it is proved that, $Δ A B C$ is an isosceles triangle.

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Given: $∠ 4 ≅ ∠ 7; ∠ 1 ≅ ∠ 3$
Prove: $Δ ABC$ is isosceles.

Short Answer

Step by step solution

– Description of step.

– Converse of isosceles triangle theorem.

– ASA postulate.

– Description of step.

– Description of step.

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Given:∠4≅∠7;∠1≅∠3Prove:ΔABC is isosceles.

Short Answer

Step by step solution

– Description of step.

– Converse of isosceles triangle theorem.

– ASA postulate.

– Description of step.

– Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Geometry

Pure Maths

Discrete Mathematics

Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Given: $∠ 4 ≅ ∠ 7; ∠ 1 ≅ ∠ 3$
Prove: $Δ ABC$ is isosceles.