Question

ab is parallel to cd. ac and bd are perpendicular to ab and cd. what is the relationship between ac and bd?
ac > bd
ac < bd
ab = cd ÷ 2
ab = cd

Explanation:

Step1: Recognize the shape

Since \(\overleftrightarrow{AB}\parallel\overleftrightarrow{CD}\), \(\overline{AC}\perp\overleftrightarrow{AB}\), \(\overline{BD}\perp\overleftrightarrow{CD}\), then \(ABDC\) is a rectangle.

Step2: Use the property of rectangle

In a rectangle, opposite sides are equal. So \(AB = CD\).

Answer:

\(AB = CD\)