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Q29

Expert-verifiedFound in: Page 170

Book edition
Student Edition

Author(s)
Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages
227 pages

ISBN
9780395977279

Given:$\u25b1\mathrm{PQRS};$ localid="1637659881844" $\overline{PJ}\cong \overline{RK}$

Prove: localid="1637659923835" $\overline{SJ}\cong \overline{QK}$

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

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 $\u25b1PQRS$.

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

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 $\u25b1PQRS$.

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

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 $\Delta SPJ\cong \Delta KRQ$.

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

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

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