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?

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

Q. If in a quadrilateral each pair of opposite angle is equal then prove that it is a parallelogram

Prove that if in a quadrilateral each pair of opposite Angles are equal then it is a parallelogram.

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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.