Which statement has a false converse?

A If a quadrilateral is a rectangle, then the diagonals of the quadrilateral are

congruent.

B If a quadrilateral has diagonals that bisect each other, then the quadrilateral is a

parallelogram

C if a quadrilateral is a rectangle, then all angles of the quadrilateral are right angles.

D If a quadrilateral is a parallelogram, then both pairs of opposite sides of the

quadrilateral are congruent.

Question

01-02-2021
Mathematics

contestada

Which statement has a false converse?

A If a quadrilateral is a rectangle, then the diagonals of the quadrilateral are

congruent.

B If a quadrilateral has diagonals that bisect each other, then the quadrilateral is a

parallelogram

C if a quadrilateral is a rectangle, then all angles of the quadrilateral are right angles.

D If a quadrilateral is a parallelogram, then both pairs of opposite sides of the

quadrilateral are congruent.

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buchinnamani208 buchinnamani208 · Answer 1 · 2021-02-04T05:35:39+01:00

Answer:

B If a quadrilateral has diagonals that bisect each other, then the quadrilateral is a parallelogram

Explanation:

A rectangle just like a square has diagonals that bisect each other and they are congruent( two lines are congruent if they are equal). A parallelogram is a quadrilateral with parallel sides and when its diagonals intersect, they are congruent too. Therefore a rectangle with diagonals that bisect each other is not necessarily a parallelogram.