Math / Geometry

QuestionGiven the following information, determine which lines, if any, are parallel. State the theorem that justifies your answer. $\angle 1 \cong \angle 6$ A) $p \| q$ ; Converse of Corresponding Angles Theorem B) $p \| q$ ; Alternate Interior Angles Converse C) $g \| h$ ; Converse of Corresponding Angles Theorem D) $g \| h$ ; Alternate Interior Angles Converse

Studdy Solution

STEP 1

1. Lines $p$ and $q$ are potentially parallel.
2. Lines $g$ and $h$ are potentially parallel.
3. There are two transversals intersecting these lines.
4. Angles $\angle 1$ and $\angle 6$ are congruent.
5. We need to determine which lines are parallel based on the given congruent angles.

STEP 2

1. Identify the position of angles 1 and 6.
2. Determine the relationship between the angles.
3. Apply the appropriate converse theorem to justify parallelism.

STEP 3

Identify the position of angles $\angle 1$ and $\angle 6$ in the diagram. Determine which lines and transversals they are associated with. Typically, angles are labeled in a way that indicates their position relative to the lines and transversals.

STEP 4

Determine the relationship between angles $\angle 1$ and $\angle 6$ . Since they are congruent, check if they are corresponding angles, alternate interior angles, or any other specific type of angle pair.

STEP 5

From the description, angles $\angle 1$ and $\angle 6$ are likely corresponding angles. Corresponding angles are on the same side of the transversal and in corresponding positions relative to the two lines.

STEP 6

Apply the appropriate converse theorem. Since angles $\angle 1$ and $\angle 6$ are corresponding angles and they are congruent, use the Converse of the Corresponding Angles Theorem. This theorem states that if two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel.

STEP 7

Based on the Converse of the Corresponding Angles Theorem, conclude that lines $g$ and $h$ are parallel. Therefore, the correct answer is:
C) $g \| h$ ; Converse of Corresponding Angles Theorem
The lines $g$ and $h$ are parallel, justified by the Converse of the Corresponding Angles Theorem.

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Studdy Solution

STEP 1

1. Lines $p$ and $q$ are potentially parallel.
2. Lines $g$ and $h$ are potentially parallel.
3. There are two transversals intersecting these lines.
4. Angles $\angle 1$ and $\angle 6$ are congruent.
5. We need to determine which lines are parallel based on the given congruent angles.

STEP 2

1. Identify the position of angles 1 and 6.
2. Determine the relationship between the angles.
3. Apply the appropriate converse theorem to justify parallelism.

STEP 3

Identify the position of angles $\angle 1$ and $\angle 6$ in the diagram. Determine which lines and transversals they are associated with. Typically, angles are labeled in a way that indicates their position relative to the lines and transversals.

STEP 4

Determine the relationship between angles $\angle 1$ and $\angle 6$ . Since they are congruent, check if they are corresponding angles, alternate interior angles, or any other specific type of angle pair.

STEP 5

From the description, angles $\angle 1$ and $\angle 6$ are likely corresponding angles. Corresponding angles are on the same side of the transversal and in corresponding positions relative to the two lines.

STEP 6

STEP 7

Based on the Converse of the Corresponding Angles Theorem, conclude that lines $g$ and $h$ are parallel. Therefore, the correct answer is:
C) $g \| h$ ; Converse of Corresponding Angles Theorem
The lines $g$ and $h$ are parallel, justified by the Converse of the Corresponding Angles Theorem.

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Studdy Solution

STEP 1

STEP 2

1. Identify the position of angles 1 and 6.2. Determine the relationship between the angles.3. Apply the appropriate converse theorem to justify parallelism.

STEP 3

Identify the position of angles ∠1 \angle 1 ∠1 and ∠6 \angle 6 ∠6 in the diagram. Determine which lines and transversals they are associated with. Typically, angles are labeled in a way that indicates their position relative to the lines and transversals.

STEP 4

Determine the relationship between angles ∠1 \angle 1 ∠1 and ∠6 \angle 6 ∠6. Since they are congruent, check if they are corresponding angles, alternate interior angles, or any other specific type of angle pair.

STEP 5

From the description, angles ∠1 \angle 1 ∠1 and ∠6 \angle 6 ∠6 are likely corresponding angles. Corresponding angles are on the same side of the transversal and in corresponding positions relative to the two lines.

STEP 6

STEP 7

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1. Identify the position of angles 1 and 6.
2. Determine the relationship between the angles.
3. Apply the appropriate converse theorem to justify parallelism.

Identify the position of angles $\angle 1$ and $\angle 6$ in the diagram. Determine which lines and transversals they are associated with. Typically, angles are labeled in a way that indicates their position relative to the lines and transversals.

Determine the relationship between angles $\angle 1$ and $\angle 6$ . Since they are congruent, check if they are corresponding angles, alternate interior angles, or any other specific type of angle pair.

From the description, angles $\angle 1$ and $\angle 6$ are likely corresponding angles. Corresponding angles are on the same side of the transversal and in corresponding positions relative to the two lines.