Q45. Write a two-column proof.聽Given... [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 3: Q45. (page 115)

Write a two-column proof.
Given: $\overset{炉}{WX} 鈯� \overset{炉}{XY}$ ;
鈭�1 is comp. to鈭�3.
笔谤辞惫别:鈭�2鈮呪垹3.

Short Answer

Expert verified

The two-column proof to prove $鈭� 2 鈮� 鈭� 3$ is:

Statement	Reason
$鈭� W X Y = 90 掳$	Given
$鈥� 鈭� 1 + 鈭� 2 = 90 掳$	Angle addition postulate
$鈥� 鈭� 1 + 鈭� 3 = 90 掳$	Given

Step by step solution

Step 1. Consider the diagram.

Here, $\overset{炉}{W X} 鈯� \overset{炉}{X Y}$ and 鈭�1 complementary to 鈭�3.

Step 2. State the proof.

From the diagram and the information:

$鈭� W X Y = 90 掳$ ... (Given)

$鈭� 1 + 鈭� 2 = 90 掳$ ... (Angle addition postulate).

$鈭� 1 + 鈭� 3 = 90 掳$ ... (Given).

Thus, $鈭� 2 鈮� 鈭� 3$ .

Step 3. State the conclusion.

Therefore, the two-column proof is:

Statement	Reason
$鈭� W X Y = 90 掳$	Given
$鈥� 鈭� 1 + 鈭� 2 = 90 掳$	Angle addition postulate
$鈥� 鈭� 1 + 鈭� 3 = 90 掳$	Given

Hence,

鈭� 2 鈮� 鈭� 3

(proved).

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91影视

Write a two-column proof.
Given: $\overset{炉}{WX} 鈯� \overset{炉}{XY}$ ;
鈭�1 is comp. to鈭�3.
笔谤辞惫别:鈭�2鈮呪垹3.

Short Answer

Step by step solution

Step 1. Consider the diagram.

Step 2. State the proof.

Step 3. State the conclusion.

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91影视

Write a two-column proof.Given: WX炉鈯�XY炉; 鈭�1 is comp. to鈭�3.笔谤辞惫别:鈭�2鈮呪垹3.

Short Answer

Step by step solution

Step 1. Consider the diagram.

Step 2. State the proof.

Step 3. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Theoretical and Mathematical Physics

Statistics

Discrete Mathematics

Geometry

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Write a two-column proof.
Given: $\overset{炉}{WX} 鈯� \overset{炉}{XY}$ ;
鈭�1 is comp. to鈭�3.
笔谤辞惫别:鈭�2鈮呪垹3.