Question

Consider the following statement:

"If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram."

This statement is a/an

1. definition
2. theorem
3. axiom
4. proposition

Answer 1

Correct Answer - Option 2 : theorem

• If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. This statement is a theorem.
• Theorem is said to be proposition that is not self-evident but that can be proved from accepted premises and so is established as a law or principle. 
• There are many properties of a parallelogram. We draw a parallelogram and draw both its diagonals intersecting at the point. Measure the lengths of these lines. We observe that the mid-point of the diagonals. Repeat this activity with some more parallelograms.
• Each time we will find that the mid-point of both the diagonal. We can use the previous concept like length, mid-points etc. Hence we can prove this theorem by accepted premises.