Question

Choose the figure(s) that is/are congruent to the shape labeled with an asterisk (*).

A. Figure a only.

B. All of the figures are congruent.

C. None of the shapes are congruent.

D. Figures a and d.

Answer 1

D. Figures a and d

Explanation:

You want to identify the shapes that are congruent.

Congruence

Shapes are congruent if corresponding angles are congruent and corresponding line segments are congruent.

Here, the designated shape appears to be a right triangle with legs of different lengths. Shapes 'a' and 'd' also appear to be right triangles, with legs approximately the same lengths as those of the starred figure.

Figures 'a' and 'd' are congruent to the starred figure.

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Additional comment

It is usual for geometry problems to rely only upon markings for congruence. That is, in general, you are not to rely upon appearance to draw conclusions about a geometry.

Here, none of the figures have any marks, so we cannot say with certainty that any of the segments or angles are congruent. Using these rules, the answer must be C. None of the shapes are congruent.

You may be able to reach a conclusion about what rules apply by looking at other problems and examples in your curriculum materials.

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