Q21 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 3: Q21 (page 82)

Write proofs in two-column form.
Given: $k 鈭� l$
Prove: $鈭� 1$ is supplementary to $鈭� 7$

Short Answer

Expert verified

Proof in two column form is

Statement	Reason
1. $k 鈭� l$	Given
2. $鈭� 4 鈮� 鈭� 7$	Vertically opposite angle
3. $m 鈭� 1 + m 鈭� 4 = 180$	Same side interior angle
4. $m 鈭� 1 + m 鈭� 7 = 180$	Substitution Property

Step by step solution

Step 1. Observations from figure

Line $t$ is transversal to the parallel lines $k$ and $I$

Step 2. Vertically opposite angle

$鈭� 4$ and $鈭� 7$ are vertically opposite angles, so they are congruent

$\begin{matrix} 鈭� 4 鈮� 鈭� 7 \\ m 鈭� 4 = m 鈭� 7 \end{matrix}$

Step 3. Same-side interior angles

$鈭� 1$ and $鈭� 4$ forms a pair of same-side interior angles

Theorem 3-3: If two parallel lines are cut by a transversal then the same-side interior angles are supplementary.

$m 鈭� 1 + m 鈭� 4 = 180$ (1)

Step 4. Use substitution property

Substitute $m 鈭� 7$ for $m 鈭� 4$ in equation (1)

$m 鈭� 1 + m 鈭� 7 = 180$

Thus, proof in two column form is

Statement	Reason
1. $k 鈭� l$	Given
2. $鈭� 4 鈮� 鈭� 7$	Vertically opposite angle
3. $m 鈭� 1 + m 鈭� 4 = 180$	Same side interior angle
4. $m 鈭� 1 + m 鈭� 7 = 180$	Substitution Property

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91影视

Write proofs in two-column form.
Given: $k 鈭� l$
Prove: $鈭� 1$ is supplementary to $鈭� 7$

Short Answer

Step by step solution

Step 1. Observations from figure

Step 2. Vertically opposite angle

Step 3. Same-side interior angles

Step 4. Use substitution property

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91影视

Write proofs in two-column form.Given: k鈭�lProve: 鈭�1is supplementary to 鈭�7

Short Answer

Step by step solution

Step 1. Observations from figure

Step 2. Vertically opposite angle

Step 3. Same-side interior angles

Step 4. Use substitution property

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Mechanics Maths

Discrete Mathematics

Logic and Functions

Decision Maths

Calculus

Study anywhere. Anytime. Across all devices.

Write proofs in two-column form.
Given: $k 鈭� l$
Prove: $鈭� 1$ is supplementary to $鈭� 7$