Transcript Chapter 10 - Mrs. Wendt

Chapter 10
Geometry
Do Now

Complete numbers 8 – 14 on page 430
Chapter 10
Lesson 6
Similar Figures
Objective:
Determine whether figures are similar
and find a missing length in a pair of
similar figures.
Geometry
The study of properties, measurement, and
relationships of points, angles, surfaces and
solids.
Similar Figures
Figures that have the same shape but
not necessarily the same size.
Corresponding sides are proportional
Corresponding angles are congruent
Congruent
Equal
~
=
A
B
AB
D
E
EF
C
F
Write each fraction in
simplest form.
H
G
1. AB
3
EF
9
2. BC
1
=
FG
3
1
=
3
Indirect measurement
Finding measurement by using similar
triangles and writing a proportion
A
D
B
ABC ~
F
E
C
DEF
Corresponding sides: AB
DE
Corresponding angles:
=
AC
DF
A ~
=
=
BC
EF
D;
~
B =
E;
C
~
=
F
A
D
6m
18 m
5m
15 m
B
C
E
F
4m
If
ABC ~
DEF, find the length of EF
Write a proportion
AC
DF
=
BC
EF
6 =
18
4
n
N=12
Kelly wants to resize a 4-inch wide by 5-inch long
photo. It is to fit in a space that is 2 inches wide.
What is the length of the resized photo in inches?
X
5 in.
2 in.
4 in.
Find the value of x in each pair of
similar figures.
A
D
6 mi
30 mi
5 mi
X
B
C
E
F
Find the value of x in each pair of
similar figures.
A
D
29.4 m
B
14 m
C
25.2 m
E
F
X
A
B
E
F
X
14 cm
G
C
31.5 cm
D
9 cm
H
Determine whether each pair of figures is similar. Justify
your answer.
A
B
6 in
E
F
18 in
G
C
D
11 in
H
33 in
Determine whether each pair of figures is
similar. Justify your answer.
A
D
21 km
B
54 km
E
18 km
63 km
If ABC  DEF, find the length of
Since the two triangles are similar, the ratios of their
corresponding sides are equal. So, you can write and
solve a proportion to find
Write a proportion.
Let n represent the length of
Then substitute.
Find the cross products.
Simplify.
Divide each side by 3.
Answer: The length of
is 16.5 centimeters.
.
If JKL  MNO, find the length of
Answer: 13.5 in.
GRID-IN TEST ITEM A rectangular picture window
12-feet long and 6-feet wide needs to be shortened to
9 feet in length to fit a redesigned wall. If the
architect wants the new window to be similar to the
old window, how wide will the new window be?
Read the Test Item
To find the width of the new window, draw a picture and
write a proportion.
Solve the Test Item
Write a proportion.
Find the cross products.
Divide each side by 12.
So, the width of the new window will be 4.5 feet.
Answer: 4.5 feet
GRID-IN TEST ITEM Tom has a rectangular garden
which has a length of 12 feet and a width of 8 feet. He
wishes to start a second garden which is similar to the
first and will have a width of 6 feet. Find the length of
the new garden.
Answer: 9
Kelly bought a miniature replica of the Statue of Liberty. The
replica is 9 inches tall, and the length of the statue’s right arm
holding the torch is 1 ¼ inches.
1. About how long is the
State of Liberty’s right
arm?
2. Kelly’s friend Bella
brought home a
smaller replica. The
length of the Statue’s
right arm is ¾ inch.
How tall is Bella’s
statue?