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Identify the Relationship Between ∠2 and ∠8 in Parallel Lines with Transversal
Mathematics (Geometry)
Grade 9 (Junior High School)
Question Content
∠2 and ∠8 are ________ because they are ________. Choose the correct option from: supplementary/alternate interior angles; supplementary/consecutive angles; congruent/consecutive angles; congruent/alternate interior angles, based on the given parallel lines and transversal diagram.
Correct Answer
congruent/alternate interior angles
Detailed Solution Steps
1
Step 1: Identify the relationship between the lines - In the diagram, lines j and k are parallel, cut by transversal l.
2
Step 2: Locate ∠2 and ∠8 - ∠2 lies between parallel lines j and k, on the upper side of transversal l; ∠8 lies between parallel lines j and k, on the lower side of transversal l, and they are on opposite sides of the transversal.
3
Step 3: Recall angle properties - Alternate interior angles are angles that lie between two parallel lines, on opposite sides of the transversal, and they are congruent (equal in measure).
4
Step 4: Match with options - ∠2 and ∠8 fit the definition of alternate interior angles, so they are congruent, which corresponds to the option 'congruent/alternate interior angles'.
Knowledge Points Involved
1
Parallel Lines and Transversals
When two parallel lines are intersected by a transversal, special angle relationships are formed. These relationships help determine if angles are congruent or supplementary, and are foundational for solving geometry problems involving parallel lines.
2
Alternate Interior Angles
Alternate interior angles are a pair of angles that lie between two parallel lines, on opposite sides of the transversal. A key theorem states that alternate interior angles formed by a transversal cutting parallel lines are congruent (have equal measure).
3
Congruent Angles
Congruent angles are angles that have the exact same measure, usually measured in degrees. In parallel line geometry, specific angle pairs (like alternate interior, alternate exterior, corresponding angles) are congruent.
4
Supplementary Angles
Supplementary angles are two angles whose measures add up to 180 degrees. Consecutive interior angles (same-side interior angles) formed by a transversal cutting parallel lines are supplementary.
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