Question

Draw several diagrams to help you decide whether each statement is true or false. If it is false, show a counterexample. It is true, draw and label a diagram you could use in a proof. List, in terms of the diagram, what is given and what is to be proved. Do not write a proof.

The diagonals of an equilateral quadrilateral are perpendicular.

Short answer

The diagonals of an equilateral quadrilateral are perpendicular isTrue.

Step-by-step solution

Step 1. Define equilateral quadrilateral.

An equilateral quadrilateral must have 4 equal sides.

Step 2. Draw the diagram.

Draw a quadrilateral Rhombus, which has four equal sides. Drawing a rhombus, ABCD, with diagonals AC and BDas shown.

Step 3. Prove if diagonals of an equilateral quadrilateral are perpendicular or not.

Since the above figure drawn is a Rhombus and the diagonals of a rhombus are perpendicular.

Therefore, the statement “the diagonals of an equilateral quadrilateral are perpendicular” is true.