Chapter 3: Q2 (page 80)

If $c ∥ d$ , name all angels that must be congruent to $∠ 1$ .

Short Answer

Expert verified

Angles congruent to $∠ 1$ is $∠ 6, ∠ 9,$ and $∠ 14$ .

Step by step solution

Step 1. Observations from figure

$a$ is transversal to parallel lines $c$ and $d$

Step 2. Find corresponding angles

Corresponding angle to $∠ 1$ is $∠ 9$

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

Thus, $∠ 1 ≅ ∠ 9$

Step 3. Find vertically opposite angles

Vertically opposite angle to $∠ 1$ is $∠ 6$

Vertically opposite angle to $∠ 9$ is $∠ 14$

Theorem 2-3: Vertically opposite angles are congruent, so $∠ 1 ≅ ∠ 6$ and $∠ 9 ≅ ∠ 14$ .

Step 4. Use transitive property

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

Substitute $∠ 1$ for $a$ , $∠ 6$ for $b$ , and $∠ 14$ for $c$

Since, $∠ 1 ≅ ∠ 6$ and $∠ 6 ≅ ∠ 14$ implies $∠ 1 ≅ ∠ 14$

Thus, angles congruent to $∠ 1$ is $∠ 6, ∠ 9,$ and $∠ 14$

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If $c ∥ d$ , name all angels that must be congruent to $∠ 1$ .

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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If c∥d, name all angels that must be congruent to ∠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

Calculus

Mechanics Maths

Logic and Functions

Probability and Statistics

Pure Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

If $c ∥ d$ , name all angels that must be congruent to $∠ 1$ .