Question

Parallelogram ABCD ​ is a rectangle.

Which statements are true?

Select each correct answer.

Responses

m∠DXC=m∠BXC
the measure of angle D X C equals the measure of angle B X C

DX=AX
D X equals A X

​ m∠ABX+m∠CBX=90° ​
​ the measure of angle A B X plus the measure of angle C B X equals 90 degrees ​

2AX=CD
2 A X equals C D

Answer 1

Assume X is the intersection of the diagonals (center of the rectangle).

True:
- DX = AX — diagonals of a rectangle are equal and bisect each other, so X is equidistant from all four vertices.
- m∠ABX + m∠CBX = 90° — at B the rays BA and BC are perpendicular, and the two angles ABX and CBX are the two parts into which BX splits the right angle ABC, so they sum to 90°.

False:
- m∠DXC = m∠BXC — these are generally supplementary (equal only in the special case of a square), not always equal for a rectangle.
- 2AX = CD — 2AX is the diagonal AC, not the side CD, so this is false.