Download 7-1 Ratios and proportions

Chapter 7 Pre-Test
 Grab your clicker
 Grab your calculator
 Clear your desk
To Start: 20 Points
 With only 2 weeks of instruction left in this
trimester, how do you feel you are currently doing
and what is your plan for success in this class for the
next couple weeks? Please respond with at least ½
page.
 After you complete the writing, please write down
vocab from section 7.1.
Chapter Seven: Similarity
Section 7-1 Ratios and Proportions
Vocabulary
 A ratio is a comparison of two quantities usually
written as a fraction, a:b, or a to b.
 A proportion is a statement that two ratios are
equal. (fraction = fraction)
 An extended proportion is when 3 or more ratios
are equal.
Properties of Proportions
a c
 is equivalent to :
b d
(1) ad  bc (cross multiplica tion  )
b d
(2) 
a c
a b
(3) 
c d
ab cd
(4)

b
d
Proportions
 Extremes and Means:
 The first and last numbers in a proportion of the extremes.
 The middle two numbers are called the Means.
Extremes
 Ex)
2:3=4:6
 Easy?
Means
Proportions
 What is the solution to
the following Proportion:
6 5

x 4
 You Try!! What is the
solution to the following
Proportion:
y4 y

9
3
3( y  4)  9 y
6(4)  5 x
24  5x
3 y  12  9 y
24
x
5
6 y  12
y2
Writing Equivalent Proportions
 In the diagram,
.
What ratio completes the
equivalent proportion of
x

y
x
6

y
7
x y

6 7
x
6
7
y
Proportions
 Two angle measures are
 Two angle measures are
in the ratio 5:9. Write
expressions for the two
angle measures in terms
of x.
in the ratio 11:7. Write
expressions for the two
angle measures in terms
of x.
 5x & 9x
 11x & 7x
Writing Equivalent Proportions
 In the diagram,
a 3

b 4
.
4
 Complete the following
3
statements:
b
4

a
3
4a  3b
a
b
b

3
4
4
a  b 77

b
44
b
a
Applications
 The perimeter of a
rectangle is 280 cm. The
ratio of the width to the
length is 3:4. What is the
length of the rectangle?
 Perimeter of a rectangle is W +
W + L + L!
 3x+3x+4x+4x=280
 14x=280
 x=20
 L=4x=80
Applications
 The lengths of the sides
of a triangle are in the
extended ratio 3:6:8.
The triangle’s perimeter
is 510 cm. What are the
lengths of the sides?
 Perimeter of a triangle is Leg1 +
Leg2 + Leg3!
 3x+6x+8x=510
 17x=510
 x=30
 Leg1=3x=90
 Leg2=6x=180
 Leg3=8x=240
Homework
 Page 436
 1-4, 9-12, 17-24, 27-32
 7-1 Worksheet
Wrap Up!!! (20 Points)
 1. Define Ratio
 2. Define Proportion
 3. Define Extended Proportion
 4. What are the Means
 5. What are the Extremes