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Home > INT1 > Chapter 7 > Lesson 7.2.3 > Problem 7-107

7-107.

For each pair of triangles below, determine whether or not the triangles are congruent. If they are congruent, show your reasoning in a flowchart. If they are not congruent, explain why not.

  1. Two triangles. First is triangle A, B, C, with interior angles 36 degrees on angle A and 42 degrees on angle C. Second is triangle X, Y, Z, with interior angles 42 degrees on angle Y and 102 degrees on angle X.

    Calculate the values of the missing angles. What do you notice?

    Does guarantee triangle congruence?

  1. 2 triangles, oriented & labeled as follows: #1, horizontal side, 10, left side, 6, right side, 7. #2, vertical side, 10, bottom left side, 7, top left side, 6.

    Does guarantee triangle congruence?

  1. Two right triangles. First is Triangle F, E, D with legs F, E, = 3 and E, D = 4. Second is triangle B, U, G with side lengths 3 on side B, U, and 5 on side B, G, the hypotenuse.

    These are both right triangles. Use the Pythagorean Theorem to calculate the lengths of the missing legs.

    Complete the proof below.
    Flow Chart with 7 ovals: #1 & 2, flow to #5, #3, & 4, flow to #6, #5 & 6 flow to #7. Labels: #1: F,E, = 3. #2: B,U, = 3. #3: F,D, = blank. #4: B,G, = 5. #5: Congruency symbol & definition of congruence. #6: Congruency symbol. #7: Triangle blank congruent triangle blank & H L congruency.

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