1. 7-3: Identifying Similar Triangles
Expectations:
G2.3.2: Use theorems about congruent triangles to prove additional theorems and solve problems.
G2.3.3: Prove that triangles are similar by SSS, SAS and AA conditions for similarity.
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2. Angle-Angle a. Draw two triangles with angle measures of 75° and 65°.
b. Label the 75° angles ∠A and ∠X.
c. Label the 65° angles ∠B and ∠Y.
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3. Angle-Angle d. Compare the ratios of corresponding sides.
e. What does this tell us about the triangles?
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4. Angle-Angle Triangle Similarity Theorem
If two angles of a first triangle are congruent to two angles of a second triangle, then the triangles are similar.
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5. Side-Side-Side a. Draw ∆ABC such that AB = 4, BC = 6 and AC = 7.
b. Draw ∆DEF such that DE = 8, EF = 12 and DF = 14.
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6. Side-Side-Side c. Compare corresponding angles.
d. What is true about the triangles?
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7. Side-Side-Side Triangle Similarity Theorem
If the measures of the corresponding sides of 2 triangles are proportional, then the triangles are similar.
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8. Side-Angle-Side a. Draw ∆KLM such that KL = 4, LM = 5 and m∠L = 60°.
b. Draw ∆RST such that RS = 8, ST = 10 and m∠S = 60°.
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9. Side-Angle-Side c. What is true about the triangles? 4/17/2017
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10. Sid-Angle-Side Triangle Similarity Theorem
If the measures of two sides of one triangle are proportional to two sides of a second triangle and the included angles are congruent, then the triangles are similar.
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11. Equality Properties of Similarity
Similarity of figures is reflexive, symmetric and transitive.
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12. Reflexive Property of Similarity
F ~ F
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13. Symmetric Property of Similarity
If F ~ G, then G ~ F.
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14. Transitive Property of Similarity
If F ~ G and G ~ H, then F ~ H.
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15. Are the following triangles similar? Justify your response.
7.2 12 12 20 9 15
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16. Are the triangles below similar? Justify with a postulate or theorem.
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17. If AB // EF, AD = 9, DB = 16, EC = 2(AE), determine AE, AC, BC and EFH F A B D
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18. Use similar triangles to answer the question below.
At 4:00 a yard stick cast a 5 foot shadow. How tall is a tree that has an 18 foot shadow at the same time?
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19. In the figure below, segment AB ⊥ segment DE
In the figure below, segment AB ⊥ segment DE. The measure of ∠CAD is equal to the measure of ∠CEB. The length of segment CA is 6 units and the length of segment CE is 187 units. If the length of segment AD is 10 units, what is the length of segment EB? 10 20 25 30 35 B D 10 C 6 18 A E
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20. Solve for x.
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21. Given: LP // MN L P J M N
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22. 4/17/2017
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23. Assignment pages 358 – 361, # 13-23 (odds), 27, 37, 39-47 (all).
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