Chapter 4: Q6. (page 133)

Write proofs in two-column form.
Given: $∠ 1 ≅ ∠ 2; ∠ 3 ≅ ∠ 4$
Prove: $Δ A D B ≅ Δ C B D$

Short Answer

Expert verified

Statement	Reason
1. $∠ 1 ≅ ∠ 2$	Given
2. $\bar{B D} ≅ \bar{B D}$	Common line segment
3. $∠ 3 ≅ ∠ 4$	Given
4. $Δ A D B ≅ Δ C B D$	ASA congruency criteria

Step by step solution

Step 1. Show that BD¯≅BD¯.

Line segment $\bar{B D}$ is common in both triangles, by reflexive property of congruency $\bar{B D}$ is congruent to itself

$\bar{B D} ≅ \bar{B D}$

Step 2. Show that ΔADB≅ΔCBD.

From step 1 and given

$Δ A D B ≅ Δ C B D$ by ASA (Angle-Side-Angle) congruency criteria

Step 3. Write two column proof.

Statement	Reason
1. $∠ 1 ≅ ∠ 2$	Given
2. $\bar{B D} ≅ \bar{B D}$	Common line segment
3. $∠ 3 ≅ ∠ 4$	Given
4. $Δ A D B ≅ Δ C B D$	ASA congruency criteria

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Write proofs in two-column form.
Given: $∠ 1 ≅ ∠ 2; ∠ 3 ≅ ∠ 4$
Prove: $Δ A D B ≅ Δ C B D$

Short Answer

Step by step solution

Step 1. Show that BD¯≅BD¯.

Step 2. Show that ΔADB≅ΔCBD.

Step 3. Write two column proof.

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Write proofs in two-column form.Given:∠1≅∠2;∠3≅∠4Prove:ΔADB≅ΔCBD

Short Answer

Step by step solution

Step 1. Show that BD¯≅BD¯.

Step 2. Show that ΔADB≅ΔCBD.

Step 3. Write two column proof.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Geometry

Decision Maths

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Write proofs in two-column form.
Given: $∠ 1 ≅ ∠ 2; ∠ 3 ≅ ∠ 4$
Prove: $Δ A D B ≅ Δ C B D$