Question

What special type of quadrilateral has diagonals that are congruent and bisect but are not perpendicular?

Answer 1

Hint: We are going to see the definitions of some different types of quadrilaterals and then see their properties. After that, compare the properties with the question.

Complete step by step solution:
A quadrilateral is a polygon with four sides.
There are many types of quadrilaterals and each quadrilateral has its own special properties.
In this question, we are supposed to find which quadrilateral has diagonals that are congruent and bisect but are not perpendicular.
Let us discuss some quadrilaterals and their properties to find out which one has congruent diagonals and bisect but are not perpendicular.

Parallelogram: A parallelogram is a quadrilateral with four sides in which two pairs are parallel.
A parallelogram has the following properties.
 $ \bullet $ Congruent opposite angles
 $ \bullet $ Congruent opposite sides
 $ \bullet $ Diagonals bisect each other sometimes perpendicularly sometimes non-perpendicularly.
 $ \bullet $ Sometimes Congruent, sometimes non-congruent diagonals.

So, parallelogram is not the answer we are looking for.

Square: A square is a quadrilateral with all four sides congruent and all four angles congruent.
A square has the following properties.
 $ \bullet $ All four sides congruent.
 $ \bullet $ All angles right angles.
 $ \bullet $ Diagonals bisect each other perpendicularly.
 $ \bullet $ Diagonals are congruent.

Here, diagonals are congruent, but the diagonals bisect each other perpendicularly. So, square is not our answer.

Rectangle: A rectangle is a quadrilateral with two pairs of parallel sides and all internal angles right angles.
A rectangle has the following properties.
 $ \bullet $ Congruent angles
 $ \bullet $ Congruent opposite sides
 $ \bullet $ Diagonals bisect each other non-perpendicularly.
 $ \bullet $ Congruent diagonals.

Hence, Rectangle is the special type of quadrilateral that has diagonals that are congruent and bisect but are not perpendicular.

Note: In geometry, a quadrilateral can be defined as a closed, two-dimensional shape which has four straight sides. The polygon has four vertices or corners. We can find the shape of quadrilaterals in various things around us, like in a chess board, a deck of cards, a kite, a tub of popcorn, a sign board and in an arrow