Math / Geometry

QuestionREL-10. Are the following lines parallel? YES or NO or MAYBE. Use the angles to help you decide. Be sure to justify your answer (ie if alt int $\cong$ then lines parallel) a. b. c.

Studdy Solution

STEP 1

What is this asking? Do the given angle pairs tell us if the lines are parallel? Watch out! Don't mix up the angle relationships!
Corresponding, alternate interior, and same-side interior angles have different rules.

STEP 2

1. Analyze Diagram A
2. Analyze Diagram B
3. Analyze Diagram C

STEP 3

Alright, in diagram A, we've got two angles: $125^\circ$ and $55^\circ$ .
These angles are sitting on the same side of the transversal and they're outside the two lines.
These are called corresponding angles, and if the lines are parallel, corresponding angles are congruent, or equal!

STEP 4

Let's see if they add up to $180^\circ$ . $125^\circ + 55^\circ = 180^\circ$ .
Woah, they add up to $180^\circ$ !
Since they're supplementary, and they're in the right spot, the lines are parallel!

STEP 5

Diagram B gives us angles of $95^\circ$ and $82^\circ$ .
These are also corresponding angles.

STEP 6

If the lines are parallel, these angles should be equal, but $95^\circ \ne 82^\circ$ .
Since the corresponding angles aren't congruent, the lines are not parallel!

STEP 7

Diagram C shows two angles, both measuring $46^\circ$ .
These are alternate interior angles, meaning they're on opposite sides of the transversal and between the two lines.

STEP 8

If the lines are parallel, alternate interior angles should be congruent.
Since both angles are $46^\circ$ , they are congruent!
This tells us the lines are parallel!

STEP 9

a. YES, the lines are parallel because the corresponding angles are supplementary. b. NO, the lines are not parallel because the corresponding angles are not congruent. c. YES, the lines are parallel because the alternate interior angles are congruent.

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QuestionREL-10. Are the following lines parallel? YES or NO or MAYBE. Use the angles to help you decide. Be sure to justify your answer (ie if alt int $\cong$ then lines parallel) a. b. c.

Studdy Solution

STEP 1

What is this asking? Do the given angle pairs tell us if the lines are parallel? Watch out! Don't mix up the angle relationships!
Corresponding, alternate interior, and same-side interior angles have different rules.

STEP 2

1. Analyze Diagram A
2. Analyze Diagram B
3. Analyze Diagram C

STEP 3

Alright, in diagram A, we've got two angles: $125^\circ$ and $55^\circ$ .
These angles are sitting on the same side of the transversal and they're outside the two lines.
These are called corresponding angles, and if the lines are parallel, corresponding angles are congruent, or equal!

STEP 4

Let's see if they add up to $180^\circ$ . $125^\circ + 55^\circ = 180^\circ$ .
Woah, they add up to $180^\circ$ !
Since they're supplementary, and they're in the right spot, the lines are parallel!

STEP 5

Diagram B gives us angles of $95^\circ$ and $82^\circ$ .
These are also corresponding angles.

STEP 6

If the lines are parallel, these angles should be equal, but $95^\circ \ne 82^\circ$ .
Since the corresponding angles aren't congruent, the lines are not parallel!

STEP 7

Diagram C shows two angles, both measuring $46^\circ$ .
These are alternate interior angles, meaning they're on opposite sides of the transversal and between the two lines.

STEP 8

If the lines are parallel, alternate interior angles should be congruent.
Since both angles are $46^\circ$ , they are congruent!
This tells us the lines are parallel!

STEP 9

a. YES, the lines are parallel because the corresponding angles are supplementary. b. NO, the lines are not parallel because the corresponding angles are not congruent. c. YES, the lines are parallel because the alternate interior angles are congruent.

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QuestionREL-10. Are the following lines parallel? YES or NO or MAYBE. Use the angles to help you decide. Be sure to justify your answer (ie if alt int ≅\cong≅ then lines parallel) a. b. c.

Studdy Solution

STEP 1

What is this asking? Do the given angle pairs tell us if the lines are parallel? Watch out! Don't mix up the angle relationships!Corresponding, alternate interior, and same-side interior angles have different rules.

STEP 2

1. Analyze Diagram A2. Analyze Diagram B3. Analyze Diagram C

STEP 3

STEP 4

Let's see if they add up to 180∘180^\circ180∘. 125∘+55∘=180∘125^\circ + 55^\circ = 180^\circ125∘+55∘=180∘.Woah, they add up to 180∘180^\circ180∘!Since they're supplementary, and they're in the right spot, the lines are **parallel**!

STEP 5

Diagram B gives us angles of 95∘95^\circ95∘ and 82∘82^\circ82∘.These are also **corresponding angles**.

STEP 6

If the lines are parallel, these angles should be equal, but 95∘≠82∘95^\circ \ne 82^\circ95∘=82∘.Since the corresponding angles aren't congruent, the lines are *not* parallel!

STEP 7

Diagram C shows two angles, both measuring 46∘46^\circ46∘.These are **alternate interior angles**, meaning they're on opposite sides of the transversal and *between* the two lines.

STEP 8

If the lines are parallel, alternate interior angles should be congruent.Since both angles are 46∘46^\circ46∘, they *are* congruent!This tells us the lines are **parallel**!

STEP 9

a. YES, the lines are parallel because the corresponding angles are supplementary. b. NO, the lines are not parallel because the corresponding angles are not congruent. c. YES, the lines are parallel because the alternate interior angles are congruent.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionREL-10. Are the following lines parallel? YES or NO or MAYBE. Use the angles to help you decide. Be sure to justify your answer (ie if alt int $\cong$ then lines parallel) a. b. c.

What is this asking? Do the given angle pairs tell us if the lines are parallel? Watch out! Don't mix up the angle relationships!
Corresponding, alternate interior, and same-side interior angles have different rules.

1. Analyze Diagram A
2. Analyze Diagram B
3. Analyze Diagram C

Let's see if they add up to $180^\circ$ . $125^\circ + 55^\circ = 180^\circ$ .
Woah, they add up to $180^\circ$ !
Since they're supplementary, and they're in the right spot, the lines are parallel!

Diagram B gives us angles of $95^\circ$ and $82^\circ$ .
These are also corresponding angles.

If the lines are parallel, these angles should be equal, but $95^\circ \ne 82^\circ$ .
Since the corresponding angles aren't congruent, the lines are not parallel!

Diagram C shows two angles, both measuring $46^\circ$ .
These are alternate interior angles, meaning they're on opposite sides of the transversal and between the two lines.

If the lines are parallel, alternate interior angles should be congruent.
Since both angles are $46^\circ$ , they are congruent!
This tells us the lines are parallel!