Question

question 35 of 40
rebecca is given two triangles, $\triangle abc$ and $\triangle def$. at first glance, she thinks that the triangles are congruent. how can she use what she knows about rotations and triangle congruence to prove the triangle congruence?
a. she can rotate $\triangle abc$ $180^{circ}$ and then compare the angles and sides. she will see that the triangles are congruent by the side side side theorem.
b. she can rotate $\triangle def$ $180^{circ}$ and then compare the angles and sides. she will see that the triangles are congruent by the angle angle angle theorem.
c. she can rotate $\triangle def$ $180^{circ}$ and then compare the angles and sides. she will see that the triangles are congruent by the side angle side theorem.
d. she can rotate $\triangle abc$ $180^{circ}$ and then compare the angles and sides. she will see that the triangles are congruent by the angle side angle theorem

Explanation:

First, identify the matching parts of the triangles: $\triangle ABC$ has $AB=11$ cm, $AC=15$ cm, $\angle A=50^\circ$; $\triangle DEF$ has $DE=11$ cm, $DF=15$ cm, $\angle D=50^\circ$. These are two sides and the included angle (SAS) for each triangle. Rotating $\triangle DEF$ 180° will align its corresponding sides and angles with $\triangle ABC$, confirming congruence via the Side-Angle-Side theorem. Option A uses SSS incorrectly, B uses AAA (which does not prove congruence), D uses ASA incorrectly.

Answer:

C. She can rotate $\triangle DEF$ 180° and then compare the angles and sides. She will see that the triangles are congruent by the Side Angle Side theorem.