Chapter 5.2, Problem 6WE

To determine

To explain: how could prove that quad. $SACK$ is parallelogram.

Answer to Problem 6WE

The quadrilateral $SACK$ is a parallelogram.

Explanation of Solution

Given information:

Given figure,

Given:

  $\Delta SOK\cong \Delta COA$

Calculation:

From the figure note that,

  $\Delta SOK\cong \Delta COA$

If those two triangles are congruent then corresponding side are also equal.

This implies that,

$\begin{array}{l}SO=OA\\ KO=OA\end{array}$ ....(1)

From (1), it follows that the diagonal of quadrilateral $SC$ and $KA$ bisect each other at point $O$ .

Note that if the diagonal bisect each other in a quadrilateral then that quadrilateral is a parallelogram.

Therefore, the quadrilateral $SACK$ is a parallelogram.