Question

name: angel ocel period: date: 10/9/25 seat: geometry homework 2.01: swbat explore and define special angle relationships created when 2 parallel lines are cut by a transversal. show all work and annotations for full credit. #1.) fill in the blanks with either \parallel lines\ or \transversal line\: to determine whether we have alternate side or same side angles we look at the _, and to determine whether our angles are interior or exterior angles we look at the _. #2.) in the diagram below, a || b. a. annotate the parallel lines, then fill in the chart below: angles angle pair name relationship ∠1 and ∠3 ∠4 and ∠6 alternate interior angles ∠8 and ∠2 ∠1 and ∠4 ∠2 and ∠7 ∠3 and ∠7 b. if m∠4 = 95°, fill in all angles in the diagram.

Explanation:

Step1: Recall angle - pair relationships

When two parallel lines are cut by a transversal, different angle - pair relationships exist.

Step2: Analyze \(\angle1\) and \(\angle3\)

\(\angle1\) and \(\angle3\) are vertical angles. Vertical angles are congruent. Angle Pair Name: Vertical Angles, Relationship: Congruent.

Step3: Analyze \(\angle4\) and \(\angle6\)

As given, they are alternate interior angles. Alternate interior angles are congruent when the lines are parallel. Relationship: Congruent.

Step4: Analyze \(\angle8\) and \(\angle2\)

\(\angle8\) and \(\angle2\) are corresponding angles. Corresponding angles are congruent when the lines are parallel. Angle Pair Name: Corresponding Angles, Relationship: Congruent.

Step5: Analyze \(\angle1\) and \(\angle4\)

\(\angle1\) and \(\angle4\) are adjacent angles that form a linear - pair. Linear - pair angles are supplementary (sum to \(180^{\circ}\)). Angle Pair Name: Linear - pair, Relationship: Supplementary.

Step6: Analyze \(\angle2\) and \(\angle7\)

\(\angle2\) and \(\angle7\) are alternate exterior angles. Alternate exterior angles are congruent when the lines are parallel. Angle Pair Name: Alternate Exterior Angles, Relationship: Congruent.

Step7: Analyze \(\angle3\) and \(\angle7\)

\(\angle3\) and \(\angle7\) are corresponding angles. Corresponding angles are congruent when the lines are parallel. Angle Pair Name: Corresponding Angles, Relationship: Congruent.

Step8: Find all angles when \(m\angle4 = 95^{\circ}\)

Since \(\angle1\) and \(\angle4\) are a linear - pair, \(m\angle1=180 - 95=85^{\circ}\). \(\angle1\) and \(\angle3\) are vertical angles, so \(m\angle3 = 85^{\circ}\). \(\angle4\) and \(\angle6\) are alternate interior angles, so \(m\angle6 = 95^{\circ}\). \(\angle8\) and \(\angle2\) are corresponding angles, \(\angle4\) and \(\angle8\) are vertical angles so \(m\angle8 = 95^{\circ}\) and \(m\angle2 = 95^{\circ}\). \(\angle2\) and \(\angle7\) are alternate exterior angles, so \(m\angle7 = 95^{\circ}\). \(\angle3\) and \(\angle7\) are corresponding angles.

Angles	Angle Pair Name	Relationship
\(\angle4\) and \(\angle6\)	Alternate Interior Angles	Congruent
\(\angle8\) and \(\angle2\)	Corresponding Angles	Congruent
\(\angle1\) and \(\angle4\)	Linear - pair	Supplementary
\(\angle2\) and \(\angle7\)	Alternate Exterior Angles	Congruent
\(\angle3\) and \(\angle7\)	Corresponding Angles	Congruent

If \(m\angle4 = 95^{\circ}\), then \(m\angle1 = 85^{\circ}\), \(m\angle2 = 95^{\circ}\), \(m\angle3 = 85^{\circ}\), \(m\angle6 = 95^{\circ}\), \(m\angle7 = 95^{\circ}\), \(m\angle8 = 95^{\circ}\)

Answer:

See the above - filled table and angle - measure calculations.