Geometry Ch 6.4 - 6.6 Quiz

1. A quadrilateral with congruent and perpendicular diagonals is a square.

True

False

A quadrilateral with congruent and perpendicular diagonals is not necessarily a square. A square is a special type of quadrilateral where all sides are equal in length and all angles are right angles. While a square does have congruent and perpendicular diagonals, there are other quadrilaterals that also have congruent and perpendicular diagonals, such as a rectangle or a rhombus. Therefore, the statement is false.

Explanation

A quadrilateral with congruent and perpendicular diagonals is not necessarily a square. A square is a special type of quadrilateral where all sides are equal in length and all angles are right angles. While a square does have congruent and perpendicular diagonals, there are other quadrilaterals that also have congruent and perpendicular diagonals, such as a rectangle or a rhombus. Therefore, the statement is false.

2. Each diagonal of a kite bisects two angles of the kite.

True

False

This statement is false. Each diagonal of a kite does not bisect two angles of the kite. The diagonals of a kite are perpendicular to each other, but they do not necessarily bisect the angles of the kite.

Explanation

This statement is false. Each diagonal of a kite does not bisect two angles of the kite. The diagonals of a kite are perpendicular to each other, but they do not necessarily bisect the angles of the kite.

3. A quadrilateral with congruent diagonals is an isosceles trapezoid or rectangle.

True

False

A quadrilateral with congruent diagonals can be a kite or a square, in addition to an isosceles trapezoid or rectangle. Therefore, the statement that it is only an isosceles trapezoid or rectangle is false.

Explanation

A quadrilateral with congruent diagonals can be a kite or a square, in addition to an isosceles trapezoid or rectangle. Therefore, the statement that it is only an isosceles trapezoid or rectangle is false.