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# Triangle Congruence Practice Problems

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— McGraw-Hill Professional
Updated on Oct 3, 2011

## Triangle Congruence Practice Problems

#### PROBLEM 1

Suppose you have a perfectly rectangular field surrounded by four straight lengths of fence. You build a straight fence diagonally across this field, so the diagonal fence divides the field into two triangles. Are these triangles directly congruent? If they are not congruent, are they directly similar?

#### SOLUTION 1

It helps to draw a diagram of this situation. If you do this, you can see that the two triangles are directly congruent. Consider the theoretical images of the triangles (which, unlike the fences, you can move around in your imagination). You can rotate one of these theoretical triangles exactly 180° (π rad), either clockwise or counterclockwise, and move it a short distance upward and to the side, and it will fit exactly over the other one.

#### PROBLEM 2

Suppose you have a telescope equipped with a camera. You focus on a distant, triangular sign and take a photograph of it. Then you double the magnification of the telescope and, making sure the whole sign fits into the field of view of the camera, you take another photograph. When you get the photos developed, you see triangles in each photograph. Are these triangles directly congruent? If not, are they directly similar?

#### SOLUTION 2

In the photos, one triangle looks larger than the other. But unless there is something wrong with the telescope, or you use a star diagonal when taking one photograph and not when taking the other (a star diagonal renders an image laterally inverted), the two triangle images have the same shape in the same rotational sense. They are not directly congruent, but they are directly similar.

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