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Q33

Expert-verifiedFound in: Page 171

Book edition
Student Edition

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

Pages
227 pages

ISBN
9780395977279

Find something interesting to prove. Then prove it. Answers may vary.

Given: $\u25b1\mathrm{ABCD};\angle 1\cong \angle 2$

It is proved that $\overline{AX}\cong \overline{CY}$.

The opposite sides of a parallelogram are congruent.

In $\u25b1ABCD$, $\overline{AD}$ and $\overline{BC}$ are opposite sides. Therefore, $\overline{AD}\cong \overline{BC}$.

From the given figure, it can be observed that $\overline{AD}\parallel \overline{BC}$ and $\overline{AC}$ is a transversal then $\angle DAC$ and $\angle ACB$ are alternate interior angles such that, $\angle DAC\cong \angle ACB$.

As $\angle 1\cong \angle 2$, $\overline{AD}\cong \overline{BC}$ and $\angle DAC\cong \angle ACB$ then by ASA postulate, $\Delta DAX\cong \Delta BCY$.

As $\Delta DAX\cong \Delta BCY$, then by corresponding parts of congruent triangles, $\overline{AX}\cong \overline{CY}$.

Hence it is proved that $\overline{AX}\cong \overline{CY}$.

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