Q1 If a鈭, name all angels that m... [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: Q1 (page 80)

If $a 鈭� b$ , name all angels that must be congruent to $鈭� 1$ .

Short Answer

Expert verified

Angles congruent to $鈭� 1$ is $鈭� 3, 鈭� 6,$ and $鈭� 8$ .

Step by step solution

Step 1. Observations from figure

$c$ is transversal to parallel $a$ lines $b$ .

Step 2. Find corresponding angles

Corresponding angle to $鈭� 1$ is $鈭� 3$

Postulate 10: If two parallel lines are cut by a transversal then the corresponding angles are congruent.

Thus, $鈭� 1 鈮� 鈭� 3$

Step 3. Find vertically opposite angles

Vertically opposite angle to $鈭� 1$ is $鈭� 6$

Vertically opposite angle to $鈭� 3$ is $鈭� 8$

Theorem 2-3: Vertically opposite angles are congruent, so $鈭� 1 鈮� 鈭� 6$ and $鈭� 3 鈮� 鈭� 8$ .

Step 4. Use transitive property

If $a = b$ and $b = c$ then $a = c$

Substitute $鈭� 1$ for $a$ , $鈭� 3$ for $b$ , and $鈭� 8$ for $c$

Since, $鈭� 1 鈮� 鈭� 3$ and $鈭� 3 鈮� 鈭� 8$ implies $鈭� 1 鈮� 鈭� 8$

Thus, angles congruent to $鈭� 1$ is $鈭� 3, 鈭� 6, and 鈭� 8$

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Statements	Reasons
1. $鈭� 2 鈮� 鈭� 1$	1.
2. $鈭� 1 鈮� 鈭� 3$	2.
3. $鈭� 2 鈮� 鈭� 3$	3.
4. $l\|\| n$	4.

91影视

If $a 鈭� b$ , name all angels that must be congruent to $鈭� 1$ .

Short Answer

Step by step solution

Step 1. Observations from figure

Step 2. Find corresponding angles

Step 3. Find vertically opposite angles

Step 4. Use transitive property

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91影视

If a鈭�b, name all angels that must be congruent to 鈭�1.

Short Answer

Step by step solution

Step 1. Observations from figure

Step 2. Find corresponding angles

Step 3. Find vertically opposite angles

Step 4. Use transitive property

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Probability and Statistics

Calculus

Decision Maths

Applied Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

If $a 鈭� b$ , name all angels that must be congruent to $鈭� 1$ .