Loretta is making a quilt. Some of the pieces that she is laying along the border are shown in the diagram below.

Which of the following is a true statement?

1. EC || FD
   Correct! You identified a pair of corresponding angles that are congruent.
2. CF || DG
   Incorrect. Angle FCD and angle GDB would have to be congruent for CF and DG to be parallel.
3. EC ⊥ CF
   Incorrect. Look for a pair of corresponding angles that are congruent.
4. FD ⊥ DG
   Incorrect. Look for a pair of corresponding angles that are congruent.

In the figure below, line g is a transversal.

Which of the following is a true statement?

1. a||b and c||d
   Incorrect. If two lines are parallel, then the corresponding angles should be congruent.
2. a||b and b||d
   Incorrect. If two lines are parallel, then the corresponding angles should be congruent.
3. a||c and c||d
   Incorrect. If two lines are parallel, then the corresponding angles should be congruent.
4. a||c and b||d
   Correct! For both of these pairs of lines, consecutive exterior angles are supplementary.

In the figure below, lines m and n are parallel, and they are cut by tranversal v.

Which of the following conjectures must be true?

1. m∠2 + m∠4 = 180°
   Incorrect. When two lines are parallel, corresponding angles are congruent.
2. m∠3 + m∠8 = 180°
   Correct! Angle 8 corresponds with Angle 6, so their measures are equal. Angles 3 and 6 form a linear pair, so they are supplementary.
3. ∠2 ≅ ∠3
   Incorrect. When two lines are parallel, consecutive interior angles are supplementary.
4. ∠8 ≅ ∠5
   Incorrect. When two lines are parallel, consecutive interior angles are supplementary.

A construction engineer needs to make sure a ceiling beam is parallel to the floor beam beneath it. The engineer's diagram is shown below.

Which pair of measurements from the diagram would be sufficient to show that the beams are parallel?

1. x = y
   Incorrect. What kind of angles are represented by x and y?
2. x = z
   Incorrect. The angles represented by x and z do not share a common transversal.
3. y = w
   Incorrect. The angles represented by y and w do not share a common transversal.
4. z = w
   Correct! The angles represented by z and w are alternate interior angles. If they are congruent, then the beams are parallel.

A portion of the side of a staircase is shown in the diagram below. In the diagram, k || m || n.

Which of the following statements justifies the conclusion that ∠1 ≅ ∠2 ≅ ∠3?

1. If k || m || n are cut by transversal t, then alternate interior angles are congruent.
   Incorrect. Angles 1, 2, and 3 are all on the same side of the transversal.
2. If k || m || n are cut by transversal t, then corresponding angles are congruent.
   Correct! Angles 1, 2, and 3 are all alternate interior corresponding angles.
3. If k || m || n are cut by transversal t, then same-side interior angles are congruent.
   Incorrect. Same-side interior angles are supplementary in parallel lines, not congruent.
4. If k || m || n are cut by transversal t, then alternate exterior angles are congruent.
   Incorrect. Angles 1, 2, and 3 are all on the same side of the transversal.