Main Idea and New Vocabulary
NGSSS
Key Concept: Similar Polygons
Example 1: Identify Similar Polygons
Example 2: Find Missing Measures
Key Concept: Ratios of Similar Figures
Example 3: Find Perimeter
Five-Minute Check
• Identify similar polygons and find missing
measures of similar polygons.
• similar polygons
• corresponding parts
• scale factor
MA.8.G.2.1 Use similar triangles to solve
problems that include height and distances.
Identify Similar Polygons
Determine whether triangle DEF is similar to
triangle HJK. Explain.
First, check to see if corresponding angles are
congruent.
D  H, E  J, and F  K, so all
corresponding angles are congruent.
Identify Similar Polygons
Next, check to see if corresponding
sides are proportional.
Since
, the corresponding sides are
proportional.
Answer: Therefore, the triangles are similar.
Determine whether
the figures are
similar. Explain.
A. Yes; corresponding angles are congruent and
corresponding sides are proportional.
B. Yes; corresponding angles are congruent and
corresponding sides are congruent.
C. No; corresponding angles are congruent, but
corresponding sides are not proportional.
D. No; corresponding angles are congruent, but
corresponding sides are not congruent.
Find Missing Measures
GEOMETRY Given that rectangle LMNO ~ rectangle
GHIJ, find the missing measure.
Find the scale factor from rectangle LMNO to rectangle
GHIJ.
scale factor:
Find Missing Measures
So, a length on rectangle LMNO is
times as long
as the corresponding length on rectangle GHIJ. Let
m represent the measure of ON.
Write the equation.
m=6
Answer: m = 6
Multiply.
GEOMETRY Given that quadrilateral
KLMN ~ quadrilateral RSTU, find the missing
measure.
A. 6
B. 8
C. 10
D. 12
Find Perimeter
BILLBOARDS A model of a billboard has a side
length of 3 inches. The corresponding side on the
actual billboard is 4 feet long. The model has a
perimeter of 42 inches. What is the perimeter of
the actual billboard?
Step 1
The actual length is proportional to the
length of the model with a ratio of
.
Find the scale factor.
Convert feet to inches
and divide out units.
Find Perimeter
Step 2
Find the perimeter of the actual billboard.
perimeter of billboard = perimeter of model • scale factor
P = 42 • 16 or 672 Substitute.
Then simplify.
Answer: The perimeter of the actual billboard is
672 inches or 56 feet.
PHOTOGRAPHS A photograph has a side length
of 8 inches. The photo is enlarged to poster size
and the corresponding side on the poster is
2 feet long. The photograph has a perimeter of
36 inches. What is the perimeter of the poster?
A. 4 feet
B. 4.5 feet
C. 9 feet
D. 18 feet
Determine whether the pair of polygons is similar.
Explain.
A. Yes; corresponding sides are proportional.
B. Yes; corresponding sides are congruent.
C. No; corresponding sides are not congruent.
D. No; corresponding sides are not proportional.
The pair of polygons is similar. Find the missing
side measure.
A.
B.
C.
D.
A greeting card is 8 inches by 6 inches, but it will
have to be cut to fit in an envelope. The scale
factor from the original card to the smaller card is
5:4. Find the dimensions of the smaller card.
A.
C.
B.
D.