Download WARM-UP 2.8: PROPORTIONS AND SIMILAR FIGURES TODAY’S OBJECTIVE

WARM-UP
1. Describe how we can solve this proportion. Find the solution of x.
x 4

7 5
5 x  28
28
x
5
2.8: PROPORTIONS AND SIMILAR
FIGURES
TODAY’S OBJECTIVE
REVIEW
• We will review how to solve proportions
• Ratio: compares two numbers by division
• Use proportions to find missing lengths in similar figures
• Proportion: an equation that states that 2 ratios are equal
a
a :b
b
a c

b d
• Proportional relationship can produce an infinite number of
equivalent ratios
SOLVING PROPORTIONS
• Cross Products Property of a Proportion: cross products of a
proportion are equal
x 2

10 5
5 x  20
x4
TRY THIS PROBLEM
n 2n  4

5
6
6n  5(2n  4)
6n  10n  20
4n  20
n  5
1
ABC ~
SIMILAR FIGURES
FGH
SIMILAR FIGURES - ANGLES

shape but not
• Similar Figures: Have the same ________
size
necessarily the same ___________
angles
• In similar figures, the measures of corresponding _________
ratio
are equal and the _________
of corresponding side lengths
equal
are ______
F
A
B
C
12
G
H
18
SIMILAR FIGURES – RATIO OF SIDES
AB AC BC
•Name sides of triangles by line


FG FH GH
segments that make up that side
•The ratios are equal
F
A
B
C
12
G
AB
AC
BC


FG FH GH
B
C
12
G
2 2 2
 
3 3 3
8 10 12


12 15 18
F
A
15
12
10
8
H
18
SIMILAR FIGURES – RATIO OF SIDES
F
A
15
12
10
8
 C  H
 B  G
 A  F
15
12
10
8
• The symbol
means “is congruent to.” Congruent
angles have the same measure.
H
18
B
SIMILAR FIGURES
12
15
12
10
8
G
C
H
18
SIMILAR FIGURES
• The two figures below are similar
FGH
ABC ~
• Find the missing length by setting up a proportion
F
F
A
B
12
C
G
D
A
15
12
10
8
5
18
H
B
15 C
I
20
G
x
H
AB
BC

FG GH
5 15

20
x
5 x  300
x  60
2
SIMILAR FIGURES
SUMMARY
• The two figures below are similar
• Find the missing length by setting up a proportion
F
A
x
1.5
B
6
C
G
12
H
AB
BC

FG GH
1.5 6

x
12
18  6x
x3
• Similar figures have the same shape but not necessarily
the same size
• These figures can help measure real-world distances
indirectly
• Determine which side lengths correspond to each other in
similar figures
• When one side length is unknown, we can create a
proportion and solve for it
TONIGHT’S HOMEWORK
Complete Worksheet
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