  ### Home > CCG > Chapter 7 > Lesson 7.1.4 > Problem7-46

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

3.  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.