Notes
Similar Figures
Predict - Draw a line matching up the pairs of shapes that have the most in
common…
Vocabulary
*Similar shapes are different _________ but have equal ___________.
*Congruent means ______________.
*Corresponds means __________________.
Notation:
*If two shapes are similar ______, their sides are proportional and their angles are congruent
_______.
**Congruent angles are marked with the same number of arcs.
*Corresponding sides of similar figures can be found by using the names of the figures!
A
X
C
B
Y
Z
∆ABC ~ ∆XYZ
∠A ≅ _______
̅̅̅̅ corresponds with _______
AB
∠B ≅ _______
̅̅̅̅
BC corresponds with _______
∠C ≅ _______
̅̅̅̅
AC corresponds with _______
Symbols:
∆
∠
¯¯̅
≅
~
triangle
angle
side
congruent
similar
Using Proportions with Similar Figures
To determine if two figures are similar:
1. Create a proportion (draw four boxes!)
2. Label the names of the figures *Use your colors to help!*
3. Complete the proportion using corresponding sides
4. Cross multiply; if it is a true proportion, the figures are similar!
Guided Practice:
Z
Determine whether figures ABC and XYZ are similar.
*Remember to line up the names of the figures!
A
15 m
6m
20 m
B
C
X
Y
8m
Independent Practice:
1) Is figure LMNO similar to QRST?
L
4 in
M
Q
12 in
H
S
S
3 km
C
A
5 km
D
U
4 cm
Y
G
X
A
X
1 km
2 km
6 cm
4) Is figure XYZ similar to ABC?
5 in
T
R
5 cm
3 cm
3) Is figure ABCD similar to RSTU?
B
W
F
3 in R
9 in
T
N
O
2) Is figure FGH similar to WXY?
Z
2 in
Y
9 in
B
22.5 in
C
To find the length of a missing side using similar figures:
1. Create a proportion (draw a box!)
2. Label the names of the figures
3. Complete the proportion using corresponding sides
4. Cross multiply and divide
Guided Practice:
Z
If ABC ~ XYZ, find the length of the missing side.
A
*HINT, HINT, HINT…Line up the names of the
triangles to help you find corresponding sides!
10
4
15
B
C
X
Y
?
Independent Practice:
Find the length of the missing sides of the figures below.
1) Figure ABCD ~ Figure WXYZ
D
C
W
2 cm
2) Figure LMN ~ Figure RST
L
X
10 cm
?
16 cm
A
8 cm B
Z
Y
20 in
B
D
C
L
2 in
R
2.5 cm
X
S
K
F
10 in
8 in
x in
N
28 cm
4) Figure XYZ ~ Figure DEF
J
M
x cm
M
3) Figure ABCD ~ Figure JKLM
A
T
Z
9 in
x in
Y
E
6 in
D