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Similar Triangles

Sydni Jordan - Olivia Smith

Warren Mott High School

9B

2MMSTC 2

rade evel ontent

xpectationG. GeometryTR. Transformations and Symmetry07. Grade 705 5th Expectation

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G.TR.07.05Show that two triangles are similar

using: AA similarity

SAS similarity SSS similarity

Use these criteria to solve problems and to justify arguments.

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Terms to KnowSimilar: Whenever two or more objects have proportional sides and congruent angles

Congruent: When objects have the exact same size/shapeCorresponding: having the same relationshipAA: A way to prove triangles are similar when they have two pairs of congruent angles

SAS: Way proving triangles are similar using two pairs of proportional sides and one pair of congruent angles

SSS: Way of proving triangles are similar when they have 3 pairs of proportional sides

5 in.

5 in.

5 in.

2 in.2in .

2 in.

5 in.5 in.

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ProportionalityWhen corresponding sides of a triangle have the same ratio

3 cm 6 cm

8 cm4 cm

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AAAngle–Angle Similarity

Corresponding angles must be congruent

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AA Similarity

8

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SASSide-Angle-Side similarity

Sides have to be proportional and corresponding angles have to be congruent

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SAS

2 in.2 in3 in 3 in

11

3 in.

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SSSSide-Side-Side Similarity

Corresponding sides must be proportional

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SSS

3 in.

4 in. 5 in.

6 in.

8 in. 10 in.

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What Not To UseWrong methods to use

ASASSAAAS

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Review Proportionality

AA

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3 cm

6 cm

8 cm4 cm

16

ReviewSAS

SSS

3 in.4 in.

5 in.

6 in.

8 in.10 in.

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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_glance-7thweb_134801_7.doc>.

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1 2 3

4 5 6

Choose a Box!

21

Are these triangles similar?

4 cm

7 cm

10 cm 10 cm4 cm

7 cm

Yes

No

Return

22

For these triangles to be similar, what must the length of the missing segment be?

8 in.

4 in.

10 in.

5 in. 2 in.?

1.5 in.

2.5 in.

3.5 in.Return

23

Which method can be used to find out if these two triangles are similar?

75º 75º

3 cm

2 cm

60º

45º

AA

SSS

Return

SAS

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If you have two pairs of congruent angles in two triangles, which similarity can be used to prove that they are similar?

SAS AA SSS

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45º45º

7 in. 3.5 in.

8 in. 4 in.

Are these triangles similar?

YES

NO

Return

26

Which one is not a way to prove that triangles are similar?

AA SSA SAS

Return

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CORRECT!

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INCORRECT!