Chapter 5.2, Problem 4WE

To determine

To state: the principal that enables to deduce $SACK$ is a parallelogram.

Answer to Problem 4WE

The required theorem is,

“If the diagonal bisect each other in a quadrilateral then that quadrilateral is a parallelogram”.

Explanation of Solution

Given information:

Given figure,

Given:

$SO=\frac{1}{2}SC$ ;  $KO=\frac{1}{2}KA$

Calculation:

From the figure note that,

  $\begin{array}{l}SO=\frac{1}{2}SC\\ KO=\frac{1}{2}KA\end{array}$

It is required to state the principal definition or theorem that proves the quadrilateral $SACK$ is parallelogram.

From the above, one can note the diagonals of the quadrilateral $SACK$ bisects each other.

The expression $SO=\frac{1}{2}SC$ means that $SO=OC$

The expression $KO=\frac{1}{2}KA$ means that $KO=OA$

Therefore, the required theorem is,

“If the diagonal bisect each other in a quadrilateral then that quadrilateral is a parallelogram”.