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

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

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

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.

Proportions

Example 1

Example 2 Find value of the variable in these proportions

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

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

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

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

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

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.

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

Example 6: Similar Figures Given: ΔABC ∼ ΔDEF 1.m ∠ D = ______ 2.m ∠ B = ______ 3.Proportion: 4.Similarity Ratio = 5.y = ________ 6.If DF is 2, what is AC?

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

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

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,  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