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.

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 2Find value of the variable in these proportions

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

Map ReadingScale: 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 FiguresDetermine if these two triangles are similar. If they are, write the proportions, a similarity statement and give the similarity ratio.

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

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?

Example 7: Similar FiguresAre 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, 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