Transcript Similar Polygons

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Objective
Identify similar polygons and find
missing measures of similar polygons
Vocabulary
Polygon
A simple closed figure in a plane formed by
three or more line segments
Vocabulary
Similar
Polygons that have the same shape
 Is similar to
Vocabulary
Corresponding parts
Parts of a similar figure that “match”
Vocabulary
Congruent
Parts of a geometric figure that have the same
measure
 is congruent to
Vocabulary
Scale factor
A ratio of the lengths of two corresponding
sides of two similar polygons
Math
Symbols
angle
Math
Symbols
Segment AB
AB
Measure of AB
AB
Example 1 Identify Similar Polygons
Example 2 Find Missing Measures
Example 3 Scale Factor and Perimeter
Determine whether triangle DEF is similar to triangle
HJK. Explain your reasoning.
First, check to see if corresponding angles are congruent.
and
1/3
Next, check to see if corresponding sides are proportional.
Change ratio
to decimal
Compare the
decimals
Answer: Angles are equal and ratios of sides are equal
so triangles are similar
1/3
Determine whether triangle ABC is similar to triangle
TRI. Explain your reasoning.
T
A
C
B
I
R
Answer: Yes; corresponding angles are congruent and
1/3
Given that rectangle GHIJ ~ rectangle LMNO, write a
proportion to find the measure of
Then solve.
Small rectangle
Large rectangle
2
3
x
Define a variable for measure of NO
Write a proportion of the rectangles
from known similar sides
2/3
x
Small rectangle
Large rectangle
4
n
Write a proportion of the rectangles
from a known similar sides with the
unknown “n”
2/3
Write a proportion using the 2 ratios
2
4
=
3
x
Cross multiply
Bring down =
Bring down 2x =
2x = 3(4)
Multiply 3  4
2x = 12
Ask “what is being done to the
variable?”
The variable is being multiplied by 2
Do the inverse on both sides of the
= sign
2/3
Do the inverse on both sides of the
= sign
2
4
=
3
x
Bring down 2x = 12
2x = 3(4)
Using the fraction bar, divide both
sides by 2
Combine “like” terms
2x = 12
Bring down =
2x = 12
2
2
Combine “like” terms
1x = 6
x = 6
Use the Identify Property to multiply
1x
Bring down = 6
Answer: Measure of NO = 6
Find the measure of
2/3
Given that rectangle ABCD ~ rectangle WXYZ, write a
proportion to find the measure of
Then solve.
Answer:
= 15
2/3
MULTIPLE- CHOICE TEST ITEM A polygon has sides
2.5 times as long as a similar polygon. The smaller
polygon has a perimeter of 42 inches
inches. What is the
perimeter of the larger polygon?
polygon
A 16.8 in.
B 45 in.
C 84 in.
D 105 in.
Big Polygon
2.5
Small Polygon 1
Write a ratio (scale factor) of the
similar polygons
x
Big Polygon
Small Polygon 42
Write a ratio of the perimeters of
the similar polygons
Define a variable of the
unknown
3/3
Write a proportion of the 2 ratios
x
2.5
=
42
1
Cross multiply
1x = 2.5(42)
Bring down 1x =
1x = 105
x = 105
Multiply 2.5  42
A 16.8 in.
Bring down =
Use the Identify Property to
multiply 1  x
The variable is now by itself
B 45 in.
C 84 in.
Answer: D
3/3
D 105 in.
*
MULTIPLE- CHOICE TEST ITEM A polygon has sides
3.5 times as long as a similar polygon. The larger
polygon has a perimeter of 77 inches. What is the
perimeter of the smaller polygon?
A 22 in.
B 34 in.
C 72 in.
Answer: A
3/3
D 269.5 in.
Assignment
Lesson 4:5
Similar Polygons
3 - 14 All