Question

MULTIPLE CHOICE Question 2 Look at the drawing below. Which of the following statements, if true, would alone prove pllq? Select all that apply. There are at least two correct answers.​

Answer 1

no c is right answer

Explanation:

angle b and e should be supplementary

Answer 2

A, B and C

Explanation:

Statement A

According to the Alternate Exterior Angles Theorem, when a transversal line intersects two parallel lines, the resulting alternate exterior angles are congruent.

Given ∠c ≅ ∠f, and as ∠c and ∠f are alternate exterior angles, then p ║ q.

Statement B

According to the Corresponding Angles Postulate, when a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.

GIven ∠d ≅ ∠g, and as ∠d and ∠g are corresponding angles, then p ║ q.

Statement C

According to the Same-side Interior Angles Theorem, when two parallel lines are intersected by a transversal, the angles that are interior to the parallel lines and on the same side of the transversal line are supplementary.

Given ∠b and ∠e are supplementary, and as ∠b and ∠e are the interior angles on the same side of the transversal
`\ell`, then p ║ q.

Statement D

∠f and ∠g are a linear pair, therefore ∠f and ∠g are supplementary. However, this does not given enough information to prove p ║ q.