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Lesson 6-R

Lesson 6-R. Chapter 6 Review. Objectives. Review Chapter 6. Vocabulary. None new. Ratios and Proportions. Proportion is two ratios set equal to each other Scaling Factor is a Ratio Used in recipes to increase (sf > 1) or decrease (sf < 1) amount it makes. Top Bottom. 4 x + 2

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Lesson 6-R

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  1. Lesson 6-R Chapter 6 Review

  2. Objectives • Review Chapter 6

  3. Vocabulary • None new

  4. Ratios and Proportions • Proportion is two ratios set equal to each other • Scaling Factor is a Ratio • Used in recipes to increase (sf > 1) or decrease (sf < 1) amount it makes Top Bottom 4 x + 2 --- = -------- 4  14 = 7  (x + 2) 7 14 56 = 7x + 14 42 = 7x 6 = x cross-multiply to solve (remember distributive property with + or -)

  5. t + 3 K H 10 A B 8 16 D C 12 L J r - 3 Similar Polygons • Similar Polygons have the same shape and are different sizes based on the scaling factor (called in chapter 9, dilations – a transformation not ) • Like with congruent triangles – Order Rules! Trapezoid HJLJ ~ Trapezoid ACDB so side HJ goes with AC Remember to separate the variables with the key (constant ratio) 8 10 8 12 --- = ------- and ---- = ------------ 16 t + 3 16 r - 3 T B

  6. D D D A A A 5 5 4 4 15 15 12 12 F F F 3 E E E B B B C C C 9 Triangle Similarity Theorems

  7. D C A B J E K L 9 7 M N 20 A M y + 6 3x - 7 B N 3y 17 – x C P Parallel Lines and Proportions • Parallel lines cut the sides of a triangle (or sides of two lines) into the same ratio AB ACso ------ = ------- in ∆AED to the right BE CD T B KL is a midsegment, which meansK and L are midpoints and ∆JKL is half of ∆JMN If we have more than one variable, then look for congruent marks; otherwise, we can’t solve it.

  8. P 24 6 y Q A 4 18 S B D R C Parts of Similar Triangles • If two triangles are similar then all parts of the triangles (perimeter, medians, altitudes, etc) have to be in the same ratio as the two triangles ∆ABC ~ ∆PRQ T B Side AB matches to side PR and gives a 1 : 3 ratio. So y is 3 times 4 or 12. All parts of ∆PRQ are 3 times larger than corresponding parts of ∆ABC Reminder PS and AD are altitudes

  9. J K M L 6 x + 3 4 x Angle Bisector Theorem • An angle bisector cuts the side opposite in the same ratio as the sides that form the original angle. x x + 3 --- = -------- 4  (x + 3) = 6  x 4 6 4x + 12 = 6x 12 = 2x 6 = x B T The Ratio of JL to JK must be the same as ML to MK

  10. Summary & Homework • Summary: • Cross-multiply to solve proportions • Remember the distributive property • Order rules for matching corresponding sides of similar figures like congruent triangles • Parallel lines cut into equal ratios • All parts of similar triangles have the same ratio • Angle bisector cuts divided side into same ratio as the sides forming the angle • Homework: Study for Ch 6 Test

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