Question

Draw several diagrams to help you decide whether each statement is true or false. If it is false, show a counterexample. It is true, draw and label a diagram you could use in a proof. List, in terms of the diagram, what is given and what is to be proved. Do not write a proof.

If both pairs of opposite sides of a quadrilateral are parallel, then the diagonals bisect each other.

Short answer

The statement “If both pairs of opposite sides of a quadrilateral are parallel, then the diagonals bisect each other.” istrue.

Step-by-step solution

Step 1. Draw the diagram.

Draw three different types of parallelograms namely ABCD, PQRS and MNOP.

Step 2. Measure the diagonals.

Measure different part of their diagonals to check if these are equal to each other or not.

When measured it will be observed that, their following diagonals are measured equal to each other.

$\begin{array}{l}\left(i\right)AC=AD=BE=BD=CD\\ \left(ii\right)VY=XZ=WZ=WY=VX\\ \left(iii\right)PS=PR=QS=RT=QT\end{array}$

Step 3. State the conclusion.

Since, the diagonals when measured of different types of parallelograms were equal to each other, therefore, it can be concluded that if both pairs of opposite sides of a quadrilateral are parallel, then the diagonals bisect each other.