Download Geometry Notes G.7 Similar Polygons and Triangles Mrs. Grieser

Geometry Notes G.7 Similar Polygons and Triangles
Mrs. Grieser
Name: _______________________________ Date: _____________ Block: _______
Congruence vs. Similarity

Congruence: Same shape and size

Similarity: Same shape (we use the symbol “~” to denote similarity)

All congruent figures are similar, but not all similar figures are congruent

Similar figures: corresponding angles are  , corresponding sides are in proportion

Scale Factor: the common ratio of the corresponding side lengths in similar figures
AB BC AC
3 4 5
1 1 1


     
DE EF DF
6 8 10
2 2 2
The scale factor of the triangle at left is
1
2
(Always write scale factors in simplest form).
Examples:
a) Find the scale factor of the
figure:
b) Are the figures similar?
Use scale factor to find out:
c) DEF ~ MNP . Find x.
Perimeters and Scale Factors
Theorem: If two polygons are similar, then the ratio of their perimeters is equal to the
ratio of their corresponding side lengths.
Examples:
a) ABCDE~FGHK.
Find x and the
perimeter of
ABCDE.
b) Polygon CDEF~QRST.
Perimeter(CDEF) = 56, DE =20, RS =
15. Find Perimeter(QRST).
Geometry Notes G.7 Similar Polygons and Triangles
Mrs. Grieser Page 2
Proving Triangles Similar

Triangle Congruence: SSS, SAS, ASA, AAS, HL

Triangle Similarity: we need congruent corresponding angles or proportional sides to
guarantee same shape
Post./Theorem
AA
SSS
SAS
For Similarity…
Two ∆s are ~ when any 2 sets of corresponding angles are congruent.
Two ∆s are ~ when all 3 sets of corresponding sides are proportional.
Two ∆s are ~ when 2 sets of corresponding sides are proportional and
their included angles are congruent.
Examples AA: Find two congruent angles
a)
b)
c)
Examples SSS: Look for equal scale factors
e) Which of the following three triangles are similar?
∆s
EFG/JHK
EFG/LMN
JHK/LMN
Longest
Medium
Shortest
SSS?
Examples SAS: Look for equal scale factors and congruent angles
f)
Scale Factor
Longer Side
Scale Factor
Shorter Side
Included Angles
Congruent?
SAS?
Classic Question Using Similarity: The Flagpole Problem!
On a sunny day, you are standing in front of ERMS. A
friend measures the length of your shadow: it is 4 feet long.
She also measures the shadow of the flagpole – it is 29 feet
long. If you are 5.5 feet tall, what is the height of the
flagpole?