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Magazine Chapter 3: Q23. (page 108)
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.
If the diagonals of a quadrilateral are congruent and also perpendicular, then the quadrilateral is a regular quadrilateral.
Short Answer
If the diagonals of a quadrilateral are congruent and also perpendicular, then the quadrilateral is a regular quadrilateral isfalse.
Step by step solution
Step 1. Define regular quadrilateral.
A regular quadrilateral must have 4 equal sides, 4 equal angles and its diagonal must bisect each other.
Step 2. Draw the diagram.
Draw a quadrilateral in which diagonal and , and .
Step 3. Prove if the quadrilateral ABCD is a regular quadrilateral or not.
In above figure in quadrilateralABCD
If diagonal and, and,then it is not necessary that all four sides and their corresponding angles are equal in length and measurement.
As it is shown in above figure.
Hence, from above description it concludes that quadrilateralABCDis not regular quadrilateral.
Therefore, if the diagonals of a quadrilateral are congruent and also perpendicular, then the quadrilateral is a regular quadrilateral is false.
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