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For each figure below, determine if the two smaller triangles in each diagram are congruent. If so, write an appropriate triangle congruence statement (you do not have to make a flowchart). Then solve for . If the triangles are not congruent, explain why not.

Each set of triangles is congruent. Now show why or how.

  1. A quadrilateral divided into two triangles by a diagonal. The left side is 6 x + 6, the right side is 8 x + 2, and the bottom side is 12 x minus 2. The top and bottom sides are both marked with two tick marks. The alternate interior angles are both marked with one tick mark.

    Congruent because of , .

  1. 2 right triangles, arranged so first triangle's right angle is at top left, horizontal leg is 40, vertical leg is 9, second triangle's short leg is right section of first triangle's hypotenuse, its long leg of 40, is right of  its hypotenuse of 41, difference of first's hypotenuse & second's short leg, is labeled x.

    Congruent because of , .