Question

The diagonals of a parallelogram are congruent. Which could be the parallelogram?

trapezoid
rectangle
kite
rhombus

Answer 1

Consider definitions of parallelogram, trapezoid, rectangle, kite and rhombus.

Parallelogram is a quadrilateral with two pairs of parallel opposite sides.

Trapezoid is a quadrilateral with one pair parallel opposite sides, trapezoid is not parallelogram, so option 1 is false.

Rectangle is a parallelogram with all angles right. Rectangle has diagonals that are congruent. Option 2 is true.

Kite is a quadrilateral with two pairs of congruent adjacent sides. Kite is not parallelogram, so option 3 is false.

Rhombus is a parallelogram with all sides congruent. The diagonals of the rhombus are not congruent, but they are perpindicular bisectors of each other. Option 4 is false.

Answer: correct choice is option 2

Answer 2

A parallelogram has two pairs of parallel and congruent sides

The parallelogram that fits the given definition is (b) rectangle

From the definition of parallelograms, we can conclude that the trapezoid is not a parallelogram.

• This is so, because the opposite sides are not congruent.

Kites and rhombus are parallelograms but the diagonals of a kite and a rhombus are not equal.

• However, the diagonals of a rectangle are equal.

Hence, the parallelogram that fits the given definition is (b) rectangle

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