Question

use the figure shown. select the pairs of congruent corresponding angles. a. ∠1 and ∠4 b. ∠2 and ∠4 c. ∠4 and ∠7 d. ∠3 and ∠6 e. ∠1 and ∠7

Explanation:

To determine congruent corresponding angles, we use the definition of corresponding angles: angles that occupy the same relative position at each intersection where a straight line crosses two others (parallel lines, assumed here as the vertical lines are parallel and the transversal is the slanted line or the horizontal line).

• Option A: ∠1 and ∠4

∠1 and ∠4 are in corresponding positions relative to the transversal (the horizontal line) and the two vertical parallel lines. So they are corresponding angles and congruent (if lines are parallel, corresponding angles are congruent).

• Option B: ∠2 and ∠4

∠2 and ∠4 do not occupy the same relative position. ∠2 is below the horizontal transversal on the left, while ∠4 is above the horizontal transversal on the right. Not corresponding.

• Option C: ∠4 and ∠7

∠4 is above the horizontal transversal, ∠7 is below the vertical transversal. Not corresponding.

• Option D: ∠3 and ∠6

∠3 (below the horizontal transversal, left vertical line) and ∠6 (below the horizontal transversal, right vertical line) are corresponding angles (same relative position with respect to the horizontal transversal and vertical parallel lines). Congruent.

• Option E: ∠1 and ∠7

∠1 is above the horizontal transversal, ∠7 is below the vertical transversal. Not corresponding.

Answer:

A. ∠1 and ∠4, D. ∠3 and ∠6