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After drawing some diagrams on his paper, Stephan thinks there is something wrong with his diagram labels. Examine each diagram below and decide whether or not the triangle could exist. If it cannot exist, explain why not.

  1. Triangle with angles labeled as follows: top, 108 degrees, right bottom, 22 degrees, left bottom, 40 degrees.

    What must be the sum of the angles in a triangle?

    Impossible, because the sum of the angle measures is less than .

  1. Right triangle labeled as follows: vertical leg, 7, horizontal leg, 12, hypotenuse, 12.

    Look at the length of the hypotenuse and the length of the bottom leg. Is there something odd there?

    Impossible, because a leg cannot be congruent to the hypotenuse.