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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 6 on side B, U, and 10 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 & HL congruency.