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Q29

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Found in: Page 170

### Geometry

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

# Given:$▱\mathrm{PQRS};$ localid="1637659881844" $\overline{PJ}\cong \overline{RK}$Prove: localid="1637659923835" $\overline{SJ}\cong \overline{QK}$

It is proved that $\overline{SJ}\cong \overline{QK}$.

See the step by step solution

## Step 1. Apply property of parallelogram.

The opposite sides of a parallelogram are congruent.

From the given figure, it can be observed that $\overline{SP}$ and $\overline{RQ}$ are opposite sides of a $▱PQRS$.

Therefore, $\overline{SP}\cong \overline{RQ}$

## Step 2. Apply property of parallelogram.

The opposite angles of a parallelogram are congruent.

From the given figure, it can be observed that $\angle P$ and $\angle R$ are opposite angles of a $▱PQRS$.

Therefore, $\angle P\cong \angle R$.

## Step 3. Apply SAS postulate.

If two sides and the included angle of one triangle are congruent to two sides and included angle of another triangle, then the triangles are congruent.

Here, $\overline{PJ}\cong \overline{RK}$, $\angle P\cong \angle R$ and $\overline{SP}\cong \overline{RQ}$, then by SAS postulate $\Delta SPJ\cong \Delta KRQ$.

## Step 4. Description of step.

As $\Delta SPJ\cong \Delta KRQ$, then by corresponding parts of congruent triangles, $\overline{SJ}\cong \overline{QK}$.

Hence it is proved that $\overline{SJ}\cong \overline{QK}$.