sections 8-1/8-2: ratios/proportions/similar figures
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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. - PowerPoint PPT PresentationTRANSCRIPT
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Sections 8-1/8-2: Ratios/Proportions/Similar Figures
April 23, 2012
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Warm-up: (10 mins)Textbook: p. 414, # 1 - 17
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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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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.
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Proportions
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Example 1
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Example 2Find value of the variable in these proportions
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Scale DrawingsScale: length of 1 square = 5 ft. Find area of rooms.
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Map ReadingScale: 1:25
(inches:miles)
Find distance from Benson to Carolina Beach.
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Similar Figures
Review: Congruency Statements
ΔABC ≅ ΔHIJ. Name three pairs of congruent sides
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Similar Figures Two polygons are similar (∼) if
1. corresponding angles are congruent and 2. corresponding sides are proportional.
Similarity Ratio: ratio of the lengths of corresponding sides
Similarity Statement: specifies similar polygons, e.g. ABCD ∼ EFGH
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Example 3: Similar Figures
1) m F = __∠ Given: ABCD ∼ EFGH, complete each statement
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Example 4: Similar FiguresDetermine if these two triangles are similar. If they are, write the proportions, a similarity statement and give the similarity ratio.
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Example 5: Similar FiguresGiven LMNO ∼ QRST, find the value of x:
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Example 6: Similar FiguresGiven: ΔABC ∼ ΔDEF
1. m∠D = ______ 2. m∠B = ______3. Proportion:
4. Similarity Ratio =
5. y = ________
6. If DF is 2, what is AC?
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Example 7: Similar FiguresAre these figures similar? If so what is the similarity statement and ratio?
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Finding the height of a distant object
Find height of the tree using similarity
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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