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Sections 8-1/8-2: Ratios/Proportions/Similar Figures

Sections 8-1/8-2: Ratios/Proportions/Similar Figures. April 23, 2012. Warm-up: (10 mins). Textbook: p. 414, # 1 - 17. Sections 8-1/8-2: Ratio/Proportions/Similar Figures. Objective: Today you will learn to write ratios , solve proportions , and identify similar figures.

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Sections 8-1/8-2: Ratios/Proportions/Similar Figures

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  1. Sections 8-1/8-2: Ratios/Proportions/Similar Figures April 23, 2012

  2. Warm-up: (10 mins) Textbook: p. 414, # 1 - 17

  3. Sections 8-1/8-2: Ratio/Proportions/Similar Figures Objective: Today you will learn to write ratios, solve proportions, and identify similar figures.

  4. Ratios and Proportions • A ratio is the comparison of two quantities and can be written in many ways, e.g. a to b; a : b; • A proportion is a statement that two ratios are equal, e.g. a : b = c : d; • An extended proportion is when three or more ratios are equal, e.g.

  5. Proportions

  6. Example 1

  7. Example 2 Find value of the variable in these proportions

  8. Scale Drawings Scale: length of 1 square = 5 ft. Find area of rooms.

  9. Map Reading Scale: 1:25 (inches:miles) Find distance from Benson to Carolina Beach.

  10. Similar Figures Review: Congruency Statements ΔABC ≅ ΔHIJ. Name three pairs of congruent sides

  11. Similar Figures • Two polygons are similar (∼) if • corresponding angles are congruentand • corresponding sides are proportional. • Similarity Ratio: ratio of the lengths of corresponding sides • Similarity Statement: specifies similar polygons, e.g. ABCD ∼ EFGH

  12. Example 3: Similar Figures Given: ABCD ∼ EFGH, complete each statement 1) m∠F = __

  13. Example 4: Similar Figures Determine if these two triangles are similar. If they are, write the proportions, a similarity statement and give the similarity ratio.

  14. Example 5: Similar Figures Given LMNO ∼ QRST, find the value of x:

  15. Example 6: Similar Figures • Given: ΔABC ∼ ΔDEF • m∠D = ______ • m∠B = ______ • Proportion: • Similarity Ratio = • y = ________ • If DF is 2, what is AC?

  16. Example 7: Similar Figures Are these figures similar? If so what is the similarity statement and ratio?

  17. Finding the height of a distant object Find height of the tree using similarity

  18. Wrap-up • Today you learned to write ratios, solve proportions, and identify similar figures • Tomorrow you’ll learn to prove triangles similar and to use the Side-Splitter and Triangle-Angle-Bisector Theorems. Homework (H) • p. 418, # 2, 7-21 (odd), 25, 39-42 • p. 425, # 1-6, 7-15 (odd), 17-28, 32, 33 Homework (R) • p. 418, # 2, 12-21, 25, 39, 41 • p. 425, # 1-6, 7-15 (odd), 17-28, 48

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