Chapter 4: Q20. (page 138)

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

Step 1. Description of step.

It is given that, $∠ 4 ≅ ∠ 7$ and the angle adjacent to congruent sides are congruent, that is, width="68">∠5≅∠6.

Step 2. 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, $\bar{A L} ≅ \bar{A M}$ .

Step 3. 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 $Δ A B L ≅ Δ A C M$ .

Step 4. Description of step.

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

Step 5. 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

Step 1. Description of step.

Step 2. Converse of isosceles triangle theorem.

Step 3. ASA postulate.

Step 4. Description of step.

Step 5. Description of step.

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

Short Answer

Step by step solution

Step 1. Description of step.

Step 2. Converse of isosceles triangle theorem.

Step 3. ASA postulate.

Step 4. Description of step.

Step 5. Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Decision Maths

Theoretical and Mathematical Physics

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Calculus

Logic and Functions

Study anywhere. Anytime. Across all devices.

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