Concept explainers
Whether the given statement is true or false. Justify with a diagram.
Answer to Problem 23WE
The diagonal of a quadrilateral are congruent and also perpendicular, then the quadrilateral is a regular quadrilateral is false.
Explanation of Solution
Given information:
Given statement:
The diagonals of a quadrilateral are congruent and also perpendicular, then the quadrilateral is a regular quadrilateral.
Calculation:
Consider the following figure:
In above figure there is a quadrilateral
In which diagonal
And
To prove quadrilateral
In above figure in quadrilateral
If diagonal
Then it is not necessary that it 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 quadrilateral
Therefore, if the diagonal of a quadrilateral are congruent and also perpendicular, then the quadrilateral is a regular quadrilateral is false.
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