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Home > CCG > Chapter 7 > Lesson 7.1.4 > Problem 7-46


For each pair of triangles below, determine whether or not the triangles are similar. If they are similar, show your reasoning in a flowchart. If they are not similar, explain how you know.  

  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.

    Angle X = 102 degrees,  angle A = 36 degrees, and Angle C is equal to angle Y which is 42 degrees.  

    Angle B = 102 degrees and Angle Z = 36 degrees both by the Triangle Angle Sum Theorem.

    All three angles is the same in both triangles.

    Triangle A, B, C is similar to triangle X, Y, Z by A, A similarity.

  2. Two triangles. First has two sides, each 6 units, and the base, 10 units. The angle opposite the side, 10, has 1 tick mark. Second has the following side lengths: 5 on top side, 3 on bottom side, and 7 on right side.The angle opposite the side, 7, has 1 tick mark

    The triangles are not similar because corresponding sides do not have the same ratio. One triangle is isosceles and the other is not.

  3. 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.

    Flow Chart Proof with bubbles. Bubbles 1 & 2, point to the bubble 3. Bubble 3, points to Bubble 10. Bubbles 4 & 5, point to bubble 6. Bubble 6 points to bubble 10. Bubbles 7 and 8, point to bubble 9. Bubble 9 points at bubble 10. Bubble 10 points at bubble 11. The bubbles are: Bubble 1: Pythagorean theorem or pythagorean triplets. Side F, D = 5. Bubble 2: Given: Side B, G = 10. Bubble 3: Side F, D divided by side B, G = 5 divided by 10 = one half. Bubble 4: Given: Side F, E = 3. Bubble 5: Given: Side B, U = 6. Bubble 6: Side F, E divided by side B, U = 3 divided by 6 = one half. Bubble 7: Given: Side E, D = 4. Bubble 8: Pythagorean theorem: Side U, G = 8. Bubble 9: Side E D divided by side U G = 4 divided by 8 = one half. Bubble 10: The ratio of side F, D to side B G is equal to the ratio of side F E to side B, U which is equal to the ratio of side E, D to side U, G. Bubble 11: Triangle F, E, D is similar to triangle B, U, G. Outside of the eleventh bubble is the label S, S, S, similarity.