Q7. Write proofs in two-column form.... [FREE SOLUTION]

91影视

Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 4: Q7. (page 133)

Write proofs in two-column form.
Given: $\overset{炉}{C D} 鈮� \overset{炉}{A B}; \overset{炉}{C B} 鈮� \overset{炉}{A D}$
Prove: $鈭� 1 鈮� 鈭� 2$

Short Answer

Expert verified

Statement	Reason
1. $\overset{炉}{C D} 鈮� \overset{炉}{A B}$	Given
2. $\overset{炉}{B D} 鈮� \overset{炉}{B D}$	Common line segment
3. $\overset{炉}{C B} 鈮� \overset{炉}{A D}$	Given
4. $螖 C B D 鈮� 螖 A D B$	ASA congruency criteria
5. $鈭� 1 鈮� 鈭� 2$	Corresponding parts of congruent triangle

Step by step solution

Step 1. Show that BD¯≅BD¯.

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

$\overset{炉}{B D} 鈮� \overset{炉}{B D}$

Step 2. Show that ΔADB≅ΔCBD.

From step 1 and given

$螖 A D B 鈮� 螖 C B D$ by ASA (Angle-Side-Angle) congruency criteria

Step 3. Show that ∠1≅∠2.

Since, corresponding parts of congruent triangle are congruent

So, $鈭� 1 鈮� 鈭� 2$

Thus, two column proof is

Statement	Reason
1. $\overset{炉}{C D} 鈮� \overset{炉}{A B}$	Given
2. $\overset{炉}{B D} 鈮� \overset{炉}{B D}$	Common line segment
3. $\overset{炉}{C B} 鈮� \overset{炉}{A D}$	Given
4.localid="1649574757985" $螖 C B D 鈮� 螖 A D B$	ASA congruency criteria
5. $鈭� 1 鈮� 鈭� 2$	Corresponding parts of congruent triangle

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91影视

Write proofs in two-column form.
Given: $\overset{炉}{C D} 鈮� \overset{炉}{A B}; \overset{炉}{C B} 鈮� \overset{炉}{A D}$
Prove: $鈭� 1 鈮� 鈭� 2$

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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91影视

Write proofs in two-column form.Given:CD炉鈮�AB炉;CB炉鈮�AD炉Prove:鈭�1鈮�鈭�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

Probability and Statistics

Geometry

Logic and Functions

Applied Mathematics

Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Write proofs in two-column form.
Given: $\overset{炉}{C D} 鈮� \overset{炉}{A B}; \overset{炉}{C B} 鈮� \overset{炉}{A D}$
Prove: $鈭� 1 鈮� 鈭� 2$