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Q6

Expert-verified
Found in: Page 174

### Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279

# Suppose you know that $△SOK\cong △COA$. Explain how you could prove that quadrilateral SACK is a parallelogram.

The quadrilateral SACK is a parallelogram that can be proved by using the fact that if both diagonals of the quadrilateral bisect each other then the quadrilateral is a parallelogram.

See the step by step solution

## Step 1. Observe the given diagram.

The given diagram is:

## Step 2. Description of step.

It is being given that $△SOK\cong △COA$.

That implies it is been given that the triangles $△SOK$ and $△COA$ are the congruent triangles.

Therefore, it can be said that $SO\cong CO$ and $KO\cong AO$.

As, $SO\cong CO$ and $KO\cong AO$, therefore it can be said that SC and KA are bisecting each other.

From the diagram, it can also be noticed that SC and KA are the diagonals of the quadrilateral SACK.

That implies it has been given that diagonals of the quadrilateral SACK are bisecting each other.

## Step 3. Write the principal definition or theorem that enables you to deduce, from the information given, that quadrilateral SACK is a parallelogram.

The quadrilateral SACK is a parallelogram that can be proved by using the fact that if both diagonals of the quadrilateral bisect each other then the quadrilateral is a parallelogram.