Name
Class
Date Lesson 7-4
Similar Figures
Lesson Objective
Common Core State Standard
To identify similar figures and to use
proportions to find missing measurements
in similar figures
Geometry: 8.G.4
Vocabulary and Key Concepts
All rights reserved.
Similar Polygons If two polygons are similar polygons, then
• corresponding angles are congruent and
• lengths of corresponding sides are in proportion .
Similar figures have the same shape but not necessarily the same size.
D
Example
3
A
U
6
48
24
R
1 Identifying Similar Polygons Is rectangle ABCD
&A
&R
&B
& S
&C
& T
&D
&U
C
3
AB
DA
RS
UR
6
3
48
24
24
48
144
144
48
B
T
Next, check whether corresponding sides are in proportion.
6
d All right angles are 90° °.
6
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
similar to rectangle RSTU? Explain.
First, check whether corresponding angles are congruent.
24
S
d AB corresponds to RS . DA corresponds to UR .
d Substitute.
? 3
The corresponding sides
d Write the cross products.
d Simplify.
are
in proportion, so rectangle ABCD is
similar to rectangle RSTU.
Quick Check
1. Is rectangle EFGH similar to rectangle PQRS? Explain.
Yes; the corresponding angles are equal and the
corresponding side lengths are proportional.
68
441198_C3_Ch7_WKbk_Ver-1.indd 68
Course 3 Lesson 7-4
E 18 F
S
27
36
H 18 G
R
27
54
P
36
54
Q
Daily Notetaking Guide
10/16/12 12:40 PM
Name
Class
Date
Examples
2 Application: Design Given that rectangle EFGH is similar to
rectangle WXYZ, find t.
EF
EH
WX
WZ
9
3
12
t
t
All rights reserved.
9
EF corresponds to
WX
.
EH corresponds to
WZ
.
d Substitute.
12
9t
36
9
9
t
d
3
d Write the cross products.
Z
9
E
t
W
F
12
3
H
G
d Simplify. Then divide each side by 9.
4
Y
d Simplify.
X
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
3 Overlapping Similar Triangles RST  PSU. Find the value of d.
S
Step 1 Separate the triangles.
Step 2 Write a proportion using corresponding sides of the triangles.
SR
RT
SP
PU
12
14
21
d
d
21
12d
294
12
23d
294
12
12
d
24.5
d Write a proportion.
12
P
9
R
d Substitute.
14
14
d
T
U
S
12
R
d Write the cross products.
14
d Simplify.
T
S
21
d Divide each side by 12.
P
d Simplify.
d
U
Quick Check
2. In Example 2, if the side lengths of EFGH are doubled, will the resulting
polygon be similar to EFGH? Explain.
Yes; the corresponding sides will be proportional.
3. If ST is 13 ft in Example 3, what is the length of SU ?
22.75 ft
Daily Notetaking Guide
441198_C3_Ch7_WKbk_Ver-1.indd 69
Course 3 Lesson 7-4
69
10/10/12 5:46 PM