Chapter 5.2, Problem 3WE

To determine

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

Answer to Problem 3WE

The required theorem is,

“If the opposite sides of quadrilateral are equal and parallel, then the quadrilateral is a parallelogram”.

Explanation of Solution

Given information:

Given figure,

Given:

$\overline{SA}\cong \overline{KC}$ ;  $\overline{SA}\parallel \overline{KC}$

Calculation:

From the figure note that,

  $\begin{array}{l}SA\cong KC\\ SA\parallel AC\end{array}$

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

From the above, one can note the opposite sides of the quadrilateral $SACK$ are parallel and equal

Therefore, the required theorem is,

“If the opposite sides of quadrilateral are equal and parallel, then the quadrilateral is a parallelogram”.