Q3. Write proofs in two鈥揷olumn for... [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: Q3. (page 130)

Write proofs in two鈥揷olumn form.
3. Given: $\overset{炉}{W O} 鈮� \overset{炉}{Z O}; \overset{炉}{X O} 鈮� \overset{炉}{Y O}$
Prove: $鈭� W 鈮� 鈭� Z$

Short Answer

Expert verified

Statement	Reason
1. $\overset{炉}{W O} 鈮� \overset{炉}{Z O}$	Given
2. $鈭� W O X 鈮� 鈭� ZOY$	Vertically opposite angles
3. $\overset{炉}{X O} 鈮� \overset{炉}{Y O}$	Given
4. $螖 W O X 鈮� 螖 ZOY$	SAS congruency criteria
5. $鈭� W 鈮� 鈭� Z$	corresponding parts of congruent triangle are congruent

Step by step solution

- Observe from figure

$鈭� W O X$ and $鈭� ZOY$ are vertically opposite angles

- Show ΔWOX≅ΔZOY

Since, vertically opposite angles are congruent

$鈭� W O X 鈮� 鈭� ZOY$

Using this and given statement $螖 W O X 鈮� 螖 ZOY$ by SAS (Side-Angle-Side) congruency criteria

- Show ∠W≅∠Z

Since, corresponding parts of congruent triangle are congruent

So, $鈭� W 鈮� 鈭� Z$

Thus, two column proof is

Statement	Reason
1. $\overset{炉}{W O} 鈮� \overset{炉}{Z O}$	Given
2. $鈭� W O X 鈮� 鈭� ZOY$	Vertically opposite angles
3. $\overset{炉}{X O} 鈮� \overset{炉}{Y O}$	Given
4. $螖 W O X 鈮� 螖 ZOY$	SAS congruency criteria
5. $鈭� W 鈮� 鈭� Z$	corresponding parts of congruent triangle are congruent

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91影视

Write proofs in two鈥揷olumn form.
3. Given: $\overset{炉}{W O} 鈮� \overset{炉}{Z O}; \overset{炉}{X O} 鈮� \overset{炉}{Y O}$
Prove: $鈭� W 鈮� 鈭� Z$

Short Answer

Step by step solution

- Observe from figure

- Show ΔWOX≅ΔZOY

- Show ∠W≅∠Z

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91影视

Write proofs in two鈥揷olumn form.3. Given: WO炉鈮�ZO炉;XO炉鈮�YO炉Prove: 鈭�W鈮�鈭�Z

Short Answer

Step by step solution

- Observe from figure

- Show ΔWOX≅ΔZOY

- Show ∠W≅∠Z

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

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Geometry

Statistics

Logic and Functions

Calculus

Study anywhere. Anytime. Across all devices.

Write proofs in two鈥揷olumn form.
3. Given: $\overset{炉}{W O} 鈮� \overset{炉}{Z O}; \overset{炉}{X O} 鈮� \overset{炉}{Y O}$
Prove: $鈭� W 鈮� 鈭� Z$