Question

Parallelogram ABCD ​ is a rectangle.

Which statements are true?

Select each correct answer.

Responses

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

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

2AX=CD
2 A X equals C D

DX=AX

Answer 1

Assuming X is the intersection of the diagonals of rectangle ABCD:

- m∠ABX + m∠CBX = 90° — True. AB and BC are perpendicular (90°) and BX lies between BA and BC, so the two angles at B sum to ∠ABC = 90°.
- m∠DXC = m∠BXC — False. XB and XD are opposite rays, so ∠DXC and ∠BXC are supplements, equal only if the diagonals are perpendicular (not generally true for a rectangle).
- 2AX = CD — False. AX = 1/2 AC, so 2·AX = AC (the diagonal), not the side CD.
- DX = AX — True. In a rectangle the diagonals bisect each other, so the intersection is equidistant from all four vertices: AX = BX = CX = DX.