Congruent and Similar Figures
Objectives:
…to identify polygons that are similar and/or congruent (given either
measurements or tic and angle marks)
…to identify corresponding sides and/or angles of similar polygons
…to use proportions to determine if two figures are similar and to do
indirect measurements
Assessment Anchor:
7.A.2.2 – Solve problems using ratios, proportions, percents and/or rates
7.C.1.2 – Identify congruence and/or similarity in polygons
NOTES
Congruent Figures – figures that have the same shape and the same size.
Symbol for congruence ----->

Similar Figures – figures that have the same shape, but not necessarily the same
size.
Symbol for similarity ----->
~
Congruent figures have corresponding angles and sides that are also congruent.
Given: ABCD
A

RSTU
U
R
B
AB  RS
S
D
A   R
C   T
D   U
C
T
DA  UR
ST  BC
Congruent and Similar Figures
***TIC MARKS and ANGLE MARKS can show congruence.
Given:
XYZ  _______
Z
Y
 Z  _____
S
R
 R  _____
YZ  _____
X
TS  _____
T
Given: ABCDE

JKLMN
A
JN = _______
B
125°
CD = _______
12 ft
DE = _______
18 ft
C
120°
E
KL = _______
m  N = _____
D
m  A = _____
L
K
m  C = _____
98°
11.5 ft
M
4 ft
N
60°
J
m  K = _____
Congruent and Similar Figures
Similar figures have corresponding angles that are congruent, BUT HAVE
CORRESPONDING SIDES THAT ARE IN PROPORTION!
E
B
AB
DE
12
BC
EF
AC
DF
8
10
C
15
F
6
9
10 8

15 12
8 6

12 9
120 = 120
72 = 72
A
D
All sides are in proportion!!
Given: ABCD ~ EFGH
Find the length of FG.
A
20m
B
12m
D
Set up proportion:
C
E
16m
20 12

16 x
F
Solve proportion:
H
G
FG = _________
Given: NOP ~ QRS
R
Find the length of RS.
O
24 in
N
8 in
AB BC

EF FG
P
Q
17 in
S
20x = 192
Congruent and Similar Figures
Indirect Measurement uses similar figures to compute distances that are
difficult to measure.
Given: A tree casts a shadow that is 10 feet long. A woman who is 5 feet tall casts
a shadow that is 4 feet long. Two similar triangles are created. How tall is
the tree?
Given: A 6 foot tall man casts a shadow that is 4.5 feet long. A telephone pole
casts a shadow that is 15.6 feet long. Two similar triangles are created.
How tall is the telephone pole?