Chapter 4: Q19. (page 138)

Given: $\bar{AB} ≅ \bar{AC}$ , $\bar{AL}$ and $\bar{AM}$ trisect $∠ BAC$ . (This means $∠ 1 ≅ ∠ 2 ≅ ∠ 3$ )
Prove: $\bar{AL} ≅ \bar{AM}$

Short Answer

Expert verified

It is proved that, $\bar{A L} ≅ \bar{A M}$ .

Step by step solution

Step 1. Isosceles triangle theorem.

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

It is given that, $\bar{A B} ≅ \bar{A C}$ . Therefore, by isosceles triangle theorem, $∠ B ≅ ∠ C$ .

Step 2. 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, $∠ B ≅ ∠ C$ , $\bar{A B} ≅ \bar{A C}$ and $∠ 1 ≅ ∠ 3$ , then by ASA postulate $Δ B L A ≅ Δ C M A$ .

Step 3. Description of step.

By congruent parts of congruent triangles, $\bar{A L} ≅ \bar{A M}$ .

Hence it is proved that, $\bar{A L} ≅ \bar{A M}$ .

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Given: $\bar{AB} ≅ \bar{AC}$ , $\bar{AL}$ and $\bar{AM}$ trisect $∠ BAC$ . (This means $∠ 1 ≅ ∠ 2 ≅ ∠ 3$ )
Prove: $\bar{AL} ≅ \bar{AM}$

Short Answer

Step by step solution

Step 1. Isosceles triangle theorem.

Step 2. ASA postulate.

Step 3. Description of step.

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Given: AB¯≅AC¯, AL¯andAM¯ trisect ∠BAC. (This means ∠1≅∠2≅∠3)Prove:AL¯≅AM¯

Short Answer

Step by step solution

Step 1. Isosceles triangle theorem.

Step 2. ASA postulate.

Step 3. Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

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Given: $\bar{AB} ≅ \bar{AC}$ , $\bar{AL}$ and $\bar{AM}$ trisect $∠ BAC$ . (This means $∠ 1 ≅ ∠ 2 ≅ ∠ 3$ )
Prove: $\bar{AL} ≅ \bar{AM}$