Transcript Applied Geometry

Geometry
Lesson 7 – 2
Similar Polygons
Objective:
Use proportions to identify similar polygons.
Solve problems using the properties of similar polygons.
Similar Polygons
What does it mean to be similar?
Same shape, but not necessarily the same size.
Similar polygons
Two polygons are similar if and only if their
corresponding angles are congruent and
corresponding side lengths are proportional.
ABCD is similar to WXYZ
Means similar to
If  FGH ~ JKL, list all pairs of congruent
angles and write a proportion that relates the
corresponding sides.
Scale Factor
The ratio of the lengths of the corresponding
sides of two similar polygons
6/3 = 2
3/6 = 1/2
Kuma wants to use the rectangular photo shown as
the background for her computer’s desktop, but she
needs to resize it. Determine whether the following
rectangular images are similar. If so, write the
similarity statement and scale factor. Explain your
reasoning.
Corresponding angles
are congruent since
all are rectangles.
10 5
2
8
Not

 proportional
14 7
12 3
8 2

12 3
10 2

15 3Cont..
Since the angles are congruent and the
sides are proportional, ABCD ~ JKLM
with a scale factor of 2/3
Determine if the triangles are similar.
If so write the similarity statement
and scale factor.
Angles are congruent since
2 angles are congruent so
are the 3rd angles.
12.5 11.5 15


10
9.2 12
1.25 = 1.25
1.25 = 1.25
1.25 = 1.25
Check that all of the
proportions are true.
Yes the triangles are proportional.
 NQP ~ RST
Scale factor: 5
4
ACDF ~ VWYZ
Find x.
x 9

10 6
Make sure the right
Things are paired up.
Use your statement!
6x = 90
x = 15
Find y.
3 y 1 6

12
9
27y – 9 = 72
27y = 81
y=3
Triangle JLM ~ Triangle QST
Find x
6x  3 4

3
2
12x – 6 = 12
12x = 18
x = 1.5
Find y
3y  2 4

5
2
6y – 4 = 20
6y = 24
y=4
Theorem
Perimeter of similar polygon

If two polygons are similar, then their perimeters
are proportional to the scale factor be
If ABCDE ~ PQRST, find the scale factor of
ABCDE to PQRST and the perimeter of each
polygon.
8
Tells what the order should be
for scale factor.
4
Scale factor:
3
4 perimeter of ABCDE

3 perimeter of PQRST
4 30

3 x
Scale factor: 4/3
4x = 90 Perimeter PQRST 22.5
x = 22.5 Perimeter ABCDE 30
4
If MNPQ ~ XYZW, find the scale factor of
MNPQ to XYZW and the perimeter of each
polygon.
8
Scale factor:  2
4
2 34

1 x
2x = 34
x = 17
Scale factor: 2
Perimeter WXYZ = 17
Perimeter MNPQ = 34
Homework
Pg. 468 1 – 7 all, 8 – 26 E,
40 – 44 E, 52, 56 – 72 E