Question

Which of the following reasons would complete the proof in lines 3 and 5

Answer 1

Option B, two line perpendicular to the same line are parallel.

Explanation:

Since DA and CB are perpendicular to AB, they are considered parallel. This is like a transversal line.

Answer 2

Definition of right angles.

Explanation:

A rectangle is a parallelogram whose opposite sides are parallel to each other. Also, these opposite sides measure the same and all four sides create right angles. In this sense the reason would complete the proof in lines 3 and 5 is the "Definition of right angles". This is because by definition the rectangle is a parallelogram with a right angle, since it is a parallelogram, its opposite is also a right angle. The other angles, which are supplementary to the previous two, add up to 180º. And since they are opposite, they are the same, therefore each of the four is a right angle.

`\angle ABC = \angle BCD = \angle CDA = \angle DAB=90^(\circ)`