Question

parallelogram abcd is a rectangle. which statements are true? select each correct answer. ac = bd ab ⊥ bc ac = ab ac ⊥ bd

Explanation:

Step1: Recall properties of rectangles

In a rectangle, the diagonals are equal. So, \(AC = BD\).

Step2: Check angle between adjacent sides

In a rectangle, each angle is \(90^{\circ}\). So, \(\overline{AB}\perp\overline{BC}\).

Step3: Analyze \(AC = AB\)

In a rectangle, \(AC\) (diagonal) is longer than \(AB\) (side) by Pythagoras theorem \(AC=\sqrt{AB^{2}+BC^{2}}\), so \(AC
eq AB\).

Step4: Analyze \(\overline{AC}\perp\overline{BD}\)

In a rectangle, diagonals are equal but not perpendicular (they are perpendicular in a rhombus). So, \(\overline{AC}\) is not perpendicular to \(\overline{BD}\).

Answer:

\(AC = BD\), \(\overline{AB}\perp\overline{BC}\)