Question

​ Parallelogram ABCD ​ is a rectangle. Which statements are true? Select each correct answer. ​ m∠ABX=m∠CBX ​ 2AX=BD BC=CX AD⎯⎯⎯⎯⎯⊥CD⎯⎯⎯⎯⎯⎯
​ A) m∠ABX=m∠CBX ​   B) 2AX=BD    C) BC=CX     D) AD⎯⎯⎯⎯⎯⊥CD⎯⎯⎯⎯⎯⎯

Answer 1

Answer: The correct option are B and D.

Explanation:

It is given that ABCD is a rectangle.

A rectangle is a four sided figure in which opposite sides are parallel and equal to each other. All the interior and are equal to 90 degree.

Both diagonal are equal and intersecting each other on their midpoints.

In the given figure AC and BD are diagonals, so AC = BD. They are intersecting each other on X, so X is the midpoint of both diagonals.

$2AX=BD$

Since all the interior angles are 90 degree therefore the two consecutive sides are always perpendicular to each other.

$AD\perp CD$

Therefore the correct options are B and D.

Answer 2

B C and D are correct