# Prove parallelogram properties problem?

I so confused on this problem. What can be the answer for this? ### 2 respuestas

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What you need to prove is that opposite sides of a rectangle are parallel.  That is the definition of a parallelogram: four sides with each side parallel to its opposite side.

As labeled, that means side AD || side BC and side AB || side DC. Only response (B) ends with that fact, so that's really the only answer that can be correct.

None of the responses are proof statements, though, because they just present conclusions without stating how they were obtained.

One way you can get that AB || DC after observing that lines perpendicular to the same line (AD in this case) are parallel to each other.  That's a basic theorem (or "proposition") about parallel lines.

• Opposite sides are equal. Opposite angles are equal. The diagonals cut one another at 90 degrees. The sum of adjacent angle is 1180 degrees.

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