Download File - Olivia Smith

Similar Triangles
Sydni Jordan - Olivia Smith
Warren Mott High School
9B
1
rade
evel
ontent
xpectation
G. Geometry
TR. Transformations and
Symmetry
07. Grade 7
05 5th Expectation
MMSTC
2
G.TR.07.05
Show that two triangles are similar using:
AA similarity
SAS similarity
SSS similarity
Use these criteria to solve problems and to
justify arguments.
MMSTC
3
Terms to Know
Similar:
Whenever
two
orhave
more
objects
AA:
Congruent:
Corresponding:
way
to
When
prove
having
objects
triangles
the
same
are
the
similar
exactusing
SAS:AWay
SSS:
Way
of
proving
proving
triangles
triangles
are
are
similar
similar
have
proportional
sides
and
congruent
when
same
relationship
size/shape
they
have
two
pairs
of
two pairs
when
theyof
have
proportional
3 pairs
of
sides
proportional
and one pair
angles
angles
of congruent angles
sides
5 in.
55in.
in.
5 in.
2 in.
5 in.
2in .
2 in.
MMSTC
4
Proportionality
When corresponding sides of a
triangle have the same ratio
6 cm
3 cm
4 cm
MMSTC
8 cm
5
AA
Angle–Angle Similarity
Corresponding angles must be
congruent
MMSTC
6
AA Similarity
MMSTC
7
8
SAS
Side-Angle-Side similarity
Sides have to be proportional and
corresponding angles have to be
congruent
MMSTC
9
SAS
2 in
3 in
MMSTC
2 in.
3 in
10
3 in.
11
SSS
Side-Side-Side Similarity
Corresponding sides must be
proportional
MMSTC
12
SSS
8 in.
10 in.
4 in.
6 in.
MMSTC
5 in.
3 in.
13
What Not To Use
Wrong methods to use
ASA
SSA
AAS
14
4,000 ft.
5,000 ft
400 ft.
3,000 ft.
MMSTC
500 ft.
300 ft.
15
Review
Proportionality
6 cm
3 cm
AA
4 cm
8 cm
MMSTC
16
Review
SAS
SSS
8 in.
10 in.
6 in.
4 in.
5 in.
3 in.
17
Resources
• B, Christian. "Applying Similar Triangles to the Real
World." similartraiangles3. PBWorks, 2010. Web. 28 Feb
2012.
<http://similartriangles3.pbworks.com/w/page/23053498/
Applying Similar Triangles to the Real World>.
• Michigan. Michigan Department of Education.
Mathematics Alignment At A Glace. Michigan: Michigan,
Web.
<http://www.michigan.gov/documents/alignment_at_a_gl
ance-7thweb_134801_7.doc>.
MMSTC
18
MMSTC
19
Choose a Box!
1
2
3
4
5
6
21
Are these triangles similar?
Yes
10 cm
4 cm
7 cm
No
4 cm
Return
10 cm
7 cm
22
For these triangles to be similar,
what must the length of the
missing segment be?
1.5 in.
?
5 in.
10 in.
Return
4 in.
2 in.
8 in.
2.5 in.
3.5 in.
23
Which method can be used to find
out if these two triangles are
similar?
AA
60º
SSS
3 cm
2 cm
75º
Return
45º
75º
SAS
24
If you have two pairs of congruent
angles in two triangles, which
similarity can be used to prove that
they are similar?
SAS
Return
AA
SSS
25
Are these triangles similar?
45º
45º
8 in.
YES
4 in.
NO
7 in.
Return
3.5 in.
26
Which one is not a way to prove
that triangles are similar?
AA
Return
SSA
SAS
27
CORRECT!
28
INCORRECT!
29