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Q5

Expert-verifiedFound in: Page 124

Book edition
Student Edition

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

Pages
227 pages

ISBN
9780395977279

Decide whether you can deduce by the SSS, SAS, or ASA postulate that another triangle is congruent to $\Delta ABC$. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

**No congruence can be deduced.**

Consider the figure.

The Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

The Side-Side-Side Postulate (SSS) says triangles are congruent if three sides of one triangle are congruent to the corresponding sides of the other triangle.

SAS Postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent.

From both the triangles $\Delta ABC$ and $\Delta XYZ$, it is clear that

$\begin{array}{l}AB=XY\\ AC=XZ\end{array}$

But neither $BC=YZ$ nor any other angles are equal.

Therefore, no postulates hold for the figures.

Thus, no congruence can be deduced.

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