Similar Polygons. Informal Definition of Similar Figures Two figures are similar if they have the...
-
Upload
lora-johnston -
Category
Documents
-
view
222 -
download
0
Transcript of Similar Polygons. Informal Definition of Similar Figures Two figures are similar if they have the...
Similar Polygons
Informal Definition of Similar Figures
Two figures are similar if they have the same
shape.(They do not necessarily have the
same size.)
Formal Definition of Similar Polygons
Two polygons are similar if their corresponding angles are congruent,and(lengths of) corresponding sides are proportional.
C
A
B
E
DF1. A D
2. B E
3. C FAB
DEAC
DF
BC
EF
Proportional(Lengths of) sides are proportional iff ratios of (lengths of) corresponding sides are equal.For example:
so the sides are proportional.
5 9
7
18
10
14
C
A
B
Z
YX
18
914
7
10
5 2
The ratio of corresponding sides of similar polygons.
Example The scale factor from ABC to _____
is____.from ZYX to ABC
is____.
Scale Factor
7 9
5
18
10
14
C
A
B
Z
YX
ZYX1/2
2
Naming Similar Polygons
**Must match the corresponding letters**
S
Q
D
C
B
AR
P
ABDC ~ RPSQ
Applying the Definition - Angles
S
Q
D
C
B
AR
P
B P D SA R C Q
**Must match the corresponding vertices**
Applying the Definition - Sides
S
Q
D
C
B
AR
P**Must match the corresponding
sides**
BD
PS
AC
RQ
AB
RP
DC
SQ
Proportional means all of
the ratios are equal!
Example 1
S
Q
D
C
B
AR
P
18
14
28
248
Given
Find the lengths of the missing sides.
ABDC ~ RPSQ
AC AB
RQ
Example 1
S
Q
D
C
B
AR
P
18
14
28
248
Given
Find AC
Step 1: Write out a proportion of for the sides.
(Be sure to match up corresponding letters!)
ABDC ~ RPSQ
RP
AB8
RP
Example 1
S
Q
D
C
B
AR
P
18
14
28
248
Given
Find the lengths of
the missing sides.
Step 2: Replace the sides with the lengths from the problem.
ABDC ~ RPSQ
AC
RQ
14 18
Example 1
S
Q
D
C
B
AR
P
18
14
28
248
Given
Find the lengths of
the missing sides.
Step 3: Cross-multiply and solve.
ABDC ~ RPSQ
14
AC 8
1818 14 8AC
14 8
18AC
56
9AC
Example 1
S
Q
D
C
B
AR
P
18
14
28
248
Given ABDC ~ RPSQ
You should be able to
find CD and BD as well!
Example 2
S
Q
D
C
B
AR
P
18
14
28
248
Given
Find the scale factor of ABDC to RPSQ
ABDC ~ RPSQ
BD
28
AC
14
8
18
DC
24
Remember the scale factor is same as the ratio of the sides.
Always put the first polygon mentioned in the numerator.
BD
PS
AC
RQ
AB
RP
DC
SQ
The scale factor of ABDC to RPSQ is 4
9
Example 3
ABCD EFGH. Solve for x, y and z.
EH EF
AD AB
5
z
x
10y
15
30
20
B C
AD
F G
E
H
10
15 20
x 20
5 10
y
30 20
10z
x = 7.5
DC AB
HG EF
FG EF
BC AB
Step 1: Write a proportion using names of sides.Step 2: Substitute values.Step 3: Cross-multiply to solve.Step 4: Repeat to find other values.
y = 10 z = 15
Dilations and Scale FactorA dilation is a transformation that changes the size of an object.
The scale factor is the ratio of the lengths of the corresponding sides of two similar polygons. It indicates the relative size of one polygon compared the another.
Congruent Triangles
Are congruent triangles similar?
What is the scale factor between two congruent triangles?