Section 8 – 2
Similar Polygons
Objectives:
To identify similar polygons
To apply similar polygons
Similar Polygons:
Two polygons whose corresponding angles are
congruent and corresponding sides are
proportional.
Similarity Ratio:
The ratio of the lengths of the corresponding
sides.
Example 1
Understanding Similarity
ABCD ~ EFGH. Complete each statement.
𝑚∠E =
𝐴𝐵 𝐴𝐷
=
𝐸𝐹
𝑚∠B =
𝐺𝐻 𝐹𝐺
=
𝐶𝐷
Example 2 Determining Similarity
A) Determine whether the triangles are
similar. If they are, write the similarity statement
and give the similarity ratio.
B) Sketch ∆XYZ and ∆MNP with ∠X ≅∠M,
∠Y≅∠N, and ∠Z≅∠P. Also, XY = 12, YZ = 14,
ZX = 16, MN = 18, NP =21, and PM = 24.
Can you conclude that the two triangles are
similar? Explain.
C) Determine whether the parallelograms are
similar? Explain.
Example 3
Using Similar Figures
A)
LMNO ~ QRST. Find the value of x.
B)
LMNO ~ QRST. Find SR to the nearest tenth.
C)
If ∆ABC ~ ∆YXZ, find the value of x.
Homework:
8 – 2 Ditto
Section 8 – 2
Continued…
Objectives:
To apply similar polygons
Example 4 Real-World Connection
A) A map has the dimensions 12 in. tall by 16
in. wide. You want to reduce the map to fit on a
4 in. by 6 in. notecard. What are the dimensions
of the largest possible complete map that you
can fit on the index card?
B) You want to enlarge a 3 in. by 5 in. photo.
If you have photo paper that is 12 in. by 16 in.,
what are the dimensions of the largest complete
enlargement you can make?
C) A painting is 24 in. wide and 36 in. long.
The length of a postcard reduction of the
painting is 6 inches. How wide is the postcard?
Homework:
Textbook Page 425 – 426; #2 – 18 Even