Angles with parallel lines

Question 1

Lines AB and CD are parallel and are cut by transversal EF. At the intersection with AB the angles are numbered 1 (top‑left), 2 (top‑right), 3 (bottom‑left), 4 (bottom‑right). At the intersection with CD the angles are numbered 5 (top‑left), 6 (top‑right), 7 (bottom‑left), 8 (bottom‑right). Which pair of angles are alternate interior angles?

Accepted Answer

Angles 3 and 6

Answer

Angles 2 and 5

Answer

Angles 1 and 4

Answer

Angles 7 and 8

Question 2

In a park design, two straight walkways are drawn parallel to each other and a third walkway cuts across them, creating the marked angles ∠X and ∠Y as alternate interior angles. Which statement correctly explains why ∠X and ∠Y have the same measure?

Accepted Answer

A translation that slides the whole figure along the transversal moves ∠X exactly onto ∠Y, and a translation does not change angle size.

Answer

∠X and ∠Y lie on a straight line, so together they must add to 180°, making them equal.

Answer

∠X and ∠Y are opposite each other at the intersection, so they are vertical angles and therefore equal.

Answer

All angles around a point total 360°, so each of these angles must be 180°.

Question 3

Lines L₁ and L₂ are parallel and are cut by transversal T, creating angles ∠A and ∠B that lie on opposite sides of T and inside the two parallel lines (alternate interior angles). Which statement correctly explains why ∠A = ∠B?

Accepted Answer

If we slide the whole picture along the transversal T until the intersection with L₁ lines up with the intersection with L₂, the angle at the first intersection moves exactly onto the second angle, so they must have the same measure.

Answer

∠A and ∠B are vertical angles, and vertical angles are always equal.

Answer

Because the lines are parallel, any two angles formed by a transversal are equal.

Answer

∠A and ∠B are supplementary, so they add to 180°, which forces each of them to be 90°.

Try three questions

In a park design, two straight walkways are drawn parallel to each other and a third walkway cuts across them, creating the marked angles ∠X and ∠Y as alternate interior angles. Which statement correctly explains why ∠X and ∠Y have the same measure?

Lines L₁ and L₂ are parallel and are cut by transversal T, creating angles ∠A and ∠B that lie on opposite sides of T and inside the two parallel lines (alternate interior angles). Which statement correctly explains why ∠A = ∠B?

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