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Geometry and Trigonometry Difficulty: Medium

In triangle $D E F$ , the measure of angle $D$ is $47 degree$ and the measure of angle $E$ is $97 degree$ . In triangle $R S T$ , the measure of angle $R$ is $47 degree$ and the measure of angle $S$ is $97 degree$ . Which of the following additional pieces of information is needed to determine whether triangle $D E F$ is similar to triangle $R S T$ ?

The measure of angle $F$

The measure of angle $T$

The measure of angle $F$ and the measure of angle $T$

No additional information is needed.

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Explanation

Choice D is correct. When two angles of one triangle are congruent to two angles of another triangle, the triangles are similar. It's given that in triangle $D E F$ , the measure of angle $D$ is $47 degree$ and the measure of angle $E$ is $97 degree$ . It's also given that in triangle $R S T$ , the measure of angle $R$ is $47 degree$ and the measure of angle $S$ is $97 degree$ . It follows that angle $D$ is congruent to angle $R$ and that angle $E$ is congruent to angle $S$ . Therefore, triangle $D E F$ is similar to triangle $R S T$ and no additional information is needed.

Choice A is incorrect and may result from conceptual errors.

Choice B is incorrect and may result from conceptual errors.

Choice C is incorrect and may result from conceptual errors.