SIMILAR FIGURESObjective: Learn to determine whether figures are similar, to use scale factors and to find missing dimensions in similar figure.
SIMILAR FIGURESWhat are Similar Figure? Similar figure are figures that have the same shape but not necessarily the same size. The symbol “~” means “is similar to”
A
B
C
E
D FThese are corresponding
angles
These are corresponding
angles
CORRESPONDING ANGLESWhat are Corresponding Angles? Corresponding angles are matching angles of two or more similar figures, in the same position.
A
B
C
E
DFThese are
corresponding angles
These are corresponding sides
CORRESPONDING SIDESWhat are Corresponding Sides? Corresponding sides are matching sides of two or more similar figures, in the same position.
A
B
C
These are corresponding
angles
These are corresponding sides
E
DF
SIMILAR FIGURESSimilar 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
height of original pic
2 5
4
. 6 25.
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 4 1 8
8
. in . in
ft x ft
Find the cross productin (ft) on both sides
cancel
Solve for x
2 4 8 1 8. in x ft ft . in
6x
Write the proportion
2 4 8 1 8. x .2 4 14 4. x .
The third side of the triangle is 6 ft long
REMEMBER!
The following are matching, or corresponding:A and X
Remember!
AB and XY
BC and YZ
AC and XZ
A
C BZ Y
X
C and Z
B and Y
TRY THIS!!!Which rectangles are similar?
A B C2in
3in
3in
4in
4in
6in
Since the three figures are rectangles all the angles
are right angles.
Compare the ratios of corresponding sides to see if they are equal.
3
4
length of rect. A
length of rect. B
2
3
? width of rect. A
width of rect. B
9 8The ratios are not equal. Rectangle A is not similar to rectangle B
3
6
length of rect. A
length of rect. C
2
4
? width of rect. A
width of rect. C
12 12The ratios are equal. Rectangle A is similar to rectangle C or A~C
EXAMPLE 1:
EXAMPLE 2:
EXAMPLE 3: