Chapter 4: Q16. (page 151)

Given: $∠ 1 ≅ ∠ 2$ ; $∠ 3 ≅ ∠ 4; ∠ 5 ≅ ∠ 6$
Prove: $\bar{BC} ≅ \bar{ED}$

Short Answer

Expert verified

$Δ AGB ≅ Δ AFE$ by SAS postulate then by corresponding parts of congruent triangles $\bar{AB} ≅ \bar{AE}$ . $Δ ABC ≅ Δ AED$ by SAS postulate then corresponding parts of congruent triangles, $\bar{BC} ≅ \bar{ED}$ .

Step by step solution

Step 1. Description of step.

Consider $Δ A G B$ and $Δ A F E$ . From the given information it can be observed that $∠ 1 ≅ ∠ 2$ , $\bar{A G} ≅ \bar{A F}$ as they are the opposite sides to the angles $∠ 3 and ∠ 4$ also, $∠ 7 ≅ ∠ 8$ then by SAS postulate, $Δ A G B ≅ Δ A F E$ .

Step 2. Description of step.

As $Δ A G B ≅ Δ A F E$ then by corresponding parts of congruent triangles $\bar{A B} ≅ \bar{A E}$ .

Step 3. Description of step.

Consider $Δ A B C$ and $Δ A E D$ . From the given figure it can be observed that $\bar{A C} ≅ \bar{A D}$ as they are the opposite sides to the angles $∠ 5 and ∠ 6$ , $∠ 1 ≅ ∠ 2$ and $\bar{A B} ≅ \bar{A E}$ then by SAS postulate, $Δ A B C ≅ Δ A E D$ .

Step 4. Description of step.

As $Δ A B C ≅ Δ A E D$ then by corresponding parts of congruent triangles, $\bar{B C} ≅ \bar{E D}$ .

Step 5. Write a paragraph proof.

$Δ A G B ≅ Δ A F E$ by SAS postulate then by corresponding parts of congruent triangles $\bar{A B} ≅ \bar{A E}$ . $Δ A B C ≅ Δ A E D$ by SAS postulate then corresponding parts of congruent triangles, $\bar{B C} ≅ \bar{E D}$ .

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Given: $∠ 1 ≅ ∠ 2$ ; $∠ 3 ≅ ∠ 4; ∠ 5 ≅ ∠ 6$
Prove: $\bar{BC} ≅ \bar{ED}$

Short Answer

Step by step solution

Step 1. Description of step.

Step 2. Description of step.

Step 3. Description of step.

Step 4. Description of step.

Step 5. Write a paragraph proof.

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Given: ∠1≅∠2;∠3≅∠4;∠5≅∠6Prove:BC¯≅ED¯

Short Answer

Step by step solution

Step 1. Description of step.

Step 2. Description of step.

Step 3. Description of step.

Step 4. Description of step.

Step 5. Write a paragraph proof.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Logic and Functions

Discrete Mathematics

Decision Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

Given: $∠ 1 ≅ ∠ 2$ ; $∠ 3 ≅ ∠ 4; ∠ 5 ≅ ∠ 6$
Prove: $\bar{BC} ≅ \bar{ED}$