Subjects geometry

Angle Pairs Identification Ec67E1

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1. **Problem Statement:** Identify the type of angle pairs for the given angle pairs in the diagram with two parallel lines and a transversal. 2. **Recall definitions:** - Corresponding angles are in the same relative position at each intersection where a transversal crosses two lines. - Same-side interior angles lie on the same side of the transversal and inside the two lines. - Alternate interior angles lie on opposite sides of the transversal and inside the two lines. - Alternate exterior angles lie on opposite sides of the transversal and outside the two lines. 3. **Analyze each pair:** - ∠2 and ∠7: These are on opposite sides of the transversal and outside the two lines, so they are **alternate exterior angles**. - ∠8 and ∠3: These are on the same side of the transversal and inside the two lines, so they are **same-side interior angles**. - ∠1 and ∠5: These are in the same relative position at each intersection (top left and top right), so they are **corresponding angles**. - ∠5 and ∠4: These are on opposite sides of the transversal and inside the two lines, so they are **alternate interior angles**. - ∠6 and ∠4: These are on the same side of the transversal and inside the two lines, so they are **same-side interior angles**. 4. **Summary of answers:** - ∠2 and ∠7: alternate exterior angles - ∠8 and ∠3: same-side interior angles - ∠1 and ∠5: corresponding angles - ∠5 and ∠4: alternate interior angles - ∠6 and ∠4: same-side interior angles This completes the identification of the angle pairs as requested.