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Q5

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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

# State the principal definition or theorem that enables you to deduce, from the information given, that quadrilateral SACK is a parallelogram.$\angle SKC\cong \angle CAS$; $\angle KCA\cong \angle ASK$

The theorem that enables us to deduce from the information given, that quadrilateral SACK is a parallelogram is that if both pairs of opposite angles of the quadrilateral are congruent 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 $\angle SKC\cong \angle CAS$ and $\angle KCA\cong \angle ASK$.

That implies it has been given that both pairs of opposite angles of the quadrilateral SACK are congruent.

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

The theorem that enables us to deduce from the information given, that quadrilateral SACK is a parallelogram is that if both pairs of opposite angles of the quadrilateral are congruent then the quadrilateral is a parallelogram.