Chapter 4: Q7. (page 133)

Write proofs in two-column form.
Given: $\bar{C D} ≅ \bar{A B}; \bar{C B} ≅ \bar{A D}$
Prove: $∠ 1 ≅ ∠ 2$

Short Answer

Expert verified

Statement	Reason
1. $\bar{C D} ≅ \bar{A B}$	Given
2. $\bar{B D} ≅ \bar{B D}$	Common line segment
3. $\bar{C B} ≅ \bar{A D}$	Given
4. $Δ C B D ≅ Δ A D B$	ASA congruency criteria
5. $∠ 1 ≅ ∠ 2$	Corresponding parts of congruent triangle

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. Show that ∠1≅∠2.

Since, corresponding parts of congruent triangle are congruent

So, $∠ 1 ≅ ∠ 2$

Thus, two column proof is

Statement	Reason
1. $\bar{C D} ≅ \bar{A B}$	Given
2. $\bar{B D} ≅ \bar{B D}$	Common line segment
3. $\bar{C B} ≅ \bar{A D}$	Given
4.localid="1649574757985" $Δ C B D ≅ Δ A D B$	ASA congruency criteria
5. $∠ 1 ≅ ∠ 2$	Corresponding parts of congruent triangle

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Write proofs in two-column form.
Given: $\bar{C D} ≅ \bar{A B}; \bar{C B} ≅ \bar{A D}$
Prove: $∠ 1 ≅ ∠ 2$

Short Answer

Step by step solution

Step 1. Show that BD¯≅BD¯.

Step 2. Show that ΔADB≅ΔCBD.

Step 3. Show that ∠1≅∠2.

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Write proofs in two-column form.Given:CD¯≅AB¯;CB¯≅AD¯Prove:∠1≅∠2

Short Answer

Step by step solution

Step 1. Show that BD¯≅BD¯.

Step 2. Show that ΔADB≅ΔCBD.

Step 3. Show that ∠1≅∠2.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Applied Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Logic and Functions

Pure Maths

Study anywhere. Anytime. Across all devices.

Write proofs in two-column form.
Given: $\bar{C D} ≅ \bar{A B}; \bar{C B} ≅ \bar{A D}$
Prove: $∠ 1 ≅ ∠ 2$