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Copy these segments, and use them to make a triangle using the given angle so that the given angle is not between the 2 given sides. Draw your triangle on tracing paper. Try to make your triangle different from the triangles drawn by the other people in your group.
Imagine we know triangles have 2 pairs of corresponding, congruent side lengths and 1 pair of corresponding, congruent angles that is not between the given sides. What can we conclude?
Sometimes this is not enough information to determine that the triangles made with those measurements are congruent. These triangles have 2 pairs of congruent sides and 1 pair of congruent angles, but they are not congruent triangles.
If the longer of the 2 given sides is opposite the given angle, though, that does guarantee congruent triangles. In a right triangle, the longest side is always the hypotenuse. If we know the hypotenuse and the leg of a right triangle, we can be confident they are congruent.
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