Question

drag the tiles to the correct boxes to complete the pairs. in the figure, line a and line b are parallel. based on the figure, match each given angle with its congruent angles. angles congruent to ∠1 angles congruent to ∠2 angles congruent to ∠7 angles congruent to ∠6 ∠3,∠7,∠6 ∠3,∠7,∠2 ∠4,∠8,∠5 ∠3,∠6,∠2

Explanation:

Step1: Recall angle - congruence rules for parallel lines

When two parallel lines are cut by a transversal, vertical - angles are congruent, corresponding angles are congruent, and alternate - interior and alternate - exterior angles are congruent.

Step2: Identify congruent angles for ∠1

∠1 is congruent to ∠4 (vertical angles), ∠5 (corresponding angles), and ∠8 (alternate - exterior angles). So, angles congruent to ∠1 are ∠4, ∠8, ∠5.

Step3: Identify congruent angles for ∠2

∠2 is congruent to ∠3 (vertical angles), ∠6 (corresponding angles), and ∠7 (alternate - exterior angles). So, angles congruent to ∠2 are ∠3, ∠6, ∠7.

Step4: Identify congruent angles for ∠7

∠7 is congruent to ∠2 (alternate - exterior angles), ∠3 (alternate - interior angles), and ∠6 (vertical angles). So, angles congruent to ∠7 are ∠3, ∠7, ∠2.

Step5: Identify congruent angles for ∠6

∠6 is congruent to ∠2 (corresponding angles), ∠3 (alternate - interior angles), and ∠7 (vertical angles). So, angles congruent to ∠6 are ∠3, ∠6, ∠2.

Answer:

∠3, ∠7, ∠6 → angles congruent to ∠2
∠3, ∠7, ∠2 → angles congruent to ∠7
∠4, ∠8, ∠5 → angles congruent to ∠1
∠3, ∠6, ∠2 → angles congruent to ∠6