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Home > CCG > Chapter 7 > Lesson 7.2.4 > Problem 7-86

7-86.

For each figure below, determine if the two smaller triangles in each figure are congruent. If so, create a flowchart to explain why. Then, solve for . If the triangles are not congruent, explain why not. Redraw and label the diagrams as needed.  

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 , .

  2. Two right triangles. The short side of the second triangle is connected to the first triangle's hypotenuse. Both triangle's bases are 40. The short side of the first triangle is 9. The hypotenuse of the second triangle is 41. The hypotenuse of the first triangle is x + the short side of the second triangle.

    Congruent because of , .