Among the following theorems, converse of which statement will NOT always be true?

If a quadrilateral is a parallelogram, then each pair of opposite angles is equal

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If a quadrilateral is a parallelogram, then its diagonal divides it into two congruent triangles

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If a quadrilateral is a parallelogram, then its diagonals bisect each other

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If a quadrilateral is a parallelogram, then each pair of opposite sides is equal

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Solution

The correct option is B
If a quadrilateral is a parallelogram, then its diagonal divides it into two congruent triangles

If a quadrilateral has two congruent triangles, then the figure may not necessarily be a parallelogram. It can be a kite as well.

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Similar questions

Which of the following statements are true (T) and which are false (F) ?

(i) In a parallelogram, the diagonals are equal.

(ii) In a parallelogram, the diagonals bisect each other.

(iii) In a parallelogram, the diagonals bisect each other at right angles.

(iv) In any quadrilateral, if a pair of opposite sides is equal, it is a parallelogram.

(v) If all the angles of a quadrilateral are equal, it is a parallelogram.

(vi) If three sides of a quadrilateral are equal, it is a parallelogram.

(vii) If three angles of a quadrilateral are equal, it is a parallelogram

(viii) If all the sides of a quadrilateral are equal it is a parallelogram.

Assertion : If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
Reason : The opposite angles of a parallelogram are equal.
Which of the following is correct?

A quadrilateral ABCD is a parallelogram if and only

if(1) Its diagonals are perpendicular(2) Its diagonals bisect each other(3) One pair of its opposite sides is parallel(4) One pair of its opposite angles is equal

Q. If each diagonal of a quadrilateral divides it into two triangles to equal areas then prove that quadrilateral is a parallelogram.

Q. If the diagonals of a quadrilateral bisect each other then quadrilateral is a parallelograms. Prove it

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Among the following theorems, converse of which statement will NOT always be true?

The correct option is B If a quadrilateral is a parallelogram, then its diagonal divides it into two congruent triangles If a quadrilateral has two congruent triangles, then the figure may not necessarily be a parallelogram. It can be a kite as well.

The correct option is B
If a quadrilateral is a parallelogram, then its diagonal divides it into two congruent triangles

If a quadrilateral has two congruent triangles, then the figure may not necessarily be a parallelogram. It can be a kite as well.