Question

1. in the diagram, assuming all the lines are parallel, circle the pairs that are congruent? ∠1 ≅ ∠4 ∠5 ≅ ∠10 ∠4 ≅ ∠7 ∠6 ≅ ∠8 ∠13 ≅ ∠12 ∠15 ≅ ∠11 ∠3 ≅ ∠8 ∠12 ≅ ∠9

Explanation:

Step1: Recall congruent angles properties

When lines are parallel, vertical angles (opposite angles formed by two intersecting lines) are congruent, and corresponding angles (angles in the same relative position) are congruent.

Step2: Analyze each pair

• For \(\angle1\cong\angle4\): \(\angle1\) and \(\angle4\) are not vertical or corresponding angles. So, they are not congruent.
• For \(\angle5\cong\angle10\): They are vertical angles. Vertical angles are congruent. So, \(\angle5\cong\angle10\).
• For \(\angle4\cong\angle7\): They are vertical angles. Vertical angles are congruent. So, \(\angle4\cong\angle7\).
• For \(\angle6\cong\angle8\): They are not vertical or corresponding angles. So, they are not congruent.
• For \(\angle13\cong\angle12\): They are not vertical or corresponding angles. So, they are not congruent.
• For \(\angle15\cong\angle11\): They are vertical angles. Vertical angles are congruent. So, \(\angle15\cong\angle11\).
• For \(\angle3\cong\angle8\): They are not vertical or corresponding angles. So, they are not congruent.
• For \(\angle12\cong\angle9\): They are not vertical or corresponding angles. So, they are not congruent.

Answer:

\(\angle5\cong\angle10\), \(\angle4\cong\angle7\), \(\angle15\cong\angle11\)