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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

Expert verified

The diagonals of an equilateral quadrilateral are perpendicular isTrue.

Step by step solution

01

Step 1. Define equilateral quadrilateral.

An equilateral quadrilateral must have 4 equal sides.

02

Step 2. Draw the diagram.

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

03

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.

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