Check Point Quiz

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Check Point Quiz

• Page 429
• 1-10

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Lesson 8-3Proving Triangles Similar

• Objective 8-3.1 Use AA, SAS and SSS similarity
  statements
• Objective 8-3.2 Apply AA, SAS and SSS
  similarity statements

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Postulate 8-1 Angle-Angle Similarity Postulate
(AA)
If two angles of one triangle are congruent to
two angles of another triangle, then the
triangles are similar.
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Example Using the AA Postulate
Explain why the two triangles are similar.
Given - Angles have equal
measures
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ExampleWrite a Similarity Statement
by the Angle-Angle Similarity Postulate
Do we have enough information to find the
similarity ratio??
No, we dont know any of the side lengths
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Theorem 8-1 Side-Angle-Side Similarity Theorem
(SAS)
If an angle of one triangle is congruent to an
angle of a second triangle,
and the sides including
the two angles are proportional,
then the two triangles are similar.
AB AC QR QS
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Example Using Similarity Theorems
Both are right angles
Therefore, QRP XYZ by the SAS Theorem.
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Theorem 8-2 Side-Side-Side Similarity Theorem
(SSS)
If the corresponding sides of two triangles are
proportional, then the triangles are similar.
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Example

• Can you conclude the triangles are similar?

F
A
D
E
Yes, by SSS ?ABC ? ?FED
B
C
Can you conclude the triangles are similar?
A
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Yes, ?APJ ? ?ABC by SSS or by SAS
2
P
J
5
3.3
B
C
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Example Finding Lengths in Similar Triangles
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Find DE
Corresponding sides of similar triangles are
proportional
Substitution
2DE 30
Cross-Product Property
DE 15
Division Property of Equality
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Example

• Explain why the triangles are similar and find x

Triangles are similar by AA
5 x 6 3
5
x
110?
70?

• 6x

3
3
2.5 x
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Using Similar Triangles for Indirect Measurement
In sunlight, a cactus casts a 9-ft shadow. At
the same time a person 6 ft tall casts a 4-ft
shadow. Find the height of the cactus.
or
or
or
4x 54
x 13.5
Cactus is 13.5 ft tall.
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Homework

• Page 435
• Problems 4-18e,24,26,30-38e