Download Similar Figures - EWA Seventh Grade Eagles

SIMILAR
FIGURES
Objective: Learn to determine whether
figures are similar, to use scale factors
and to find missing dimensions in similar
figure.
SIMILAR FIGURES
 What
are Similar Figure?
Similar figure are figures that have the
same shape but not necessarily the same
size. The symbol “~” means “is similar to”
These are
B
corresponding angles
E
A
These are
corresponding angles
C
D
F
CORRESPONDING ANGLES
 What
are Corresponding Angles?
Corresponding angles are matching angles
of two or more similar figures, in the same
position.
These are
corresponding sides
B
E
A
These are
corresponding angles
C
F
D
CORRESPONDING SIDES
 What
are Corresponding Sides?
Corresponding sides are matching sides of
two or more similar figures, in the same
position.
These are
corresponding sides
B
E
A
These are
corresponding angles
C
F
D
SIMILAR FIGURES
Similar Figures
Two figures are similar if:
• The measures of their corresponding
angles are equal
• The ratios of the lengths of their
corresponding sides are proportional
The ratio formed by the corresponding
sides is the scale factor
TRY THIS!!!
A picture 4 in. tall and 9 in. wide is to be scaled
to 2.5 in. tall to be displayed on a Web page.
How wide should the picture be on the Web page
for the two pictures to be similar?
To find the scale factor, divide the known height of the scaled picture
by the corresponding height of the original picture
height of scaled pic
2.5

 6.25
height of original pic
4
Then multiply the width of the original picture by the scale factor
6.25  9   5.625
The picture should be 5.625 in. wide.
TRY THIS!!!
A company’s logo is in the shape of an isosceles triangle
with two sides that are 2.4 in. long and one side that is
1.8 in. long. On billboard, the triangle in the logo has
two sides that each 8 ft. long. What is the length of the
third side of the triangle on the billboard?
2.4in 1.8in

8 ft
x ft
Write the proportion
2.4in  x ft   8 ft 1.8in 
2.4 x  8 1.8 
2.4 x  14.4
x6
Find the cross product
in (ft) on both sides cancel
Solve for x
The third side of the triangle is 6 ft long
REMEMBER!
Remember!
A
C
X
B
Z
Y
The following are matching, or corresponding:
A and X
AB and XY
B and Y
BC and YZ
C and Z
AC and XZ
TRY THIS!!!
Which rectangles are similar?
Since the three figures are
rectangles all the angles are
right angles.
A
3in
2in
B
3in
4in
C
6in
Compare the ratios of corresponding sides to see if they are equal.
length of rect. A
3 ?2
width of rect. A
  
length of rect. B
4 3
width of rect. B
98
The ratios are not equal. Rectangle A is not similar to rectangle B
length of rect. A
3?2
width of rect. A
  
length of rect. C
6 4
width of rect. C
12  12
The ratios are equal. Rectangle A is similar to rectangle C or A~C
4in
EXAMPLE 1:
EXAMPLE 2:
EXAMPLE 3: