If diagonals of a quadrilateral bisect each other, it must be a parallelogram. State whether the statement is true or false.

Solution:

Given, If diagonals of a quadrilateral bisect each other, it must be a parallelogram.

We have to determine if the given statement is true or false.

A parallelogram is defined as a quadrilateral in which both pairs of opposite sides are parallel and equal.

The properties of a parallelogram are

1. The opposite sides are parallel and congruent

2. The opposite angles are congruent

3. The consecutive angles are supplementary

4. If any one of the angles is a right angle, then all the other angles will be at right angle

5. The two diagonals bisect each other

6. Each diagonal bisects the parallelogram into two congruent triangles

7. The Sum of squares of all the sides of a parallelogram is equal to the sum of squares of its diagonals. It is also called parallelogram law.

Therefore, the diagonals of a parallelogram bisect each other.

✦ Try This: If diagonals of a quadrilateral bisect each other, it must be a square. State whether the statement is true or false.

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Problem 128

If diagonals of a quadrilateral bisect each other, it must be a parallelogram. State whether the statement is true or false.

Summary:

The given statement, ”If diagonals of a quadrilateral bisect each other, it must be a parallelogram” is true.

☛ Related Questions:

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