Download - Objectives
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Objectives
• Prove that two triangles are similar using AA, SAS, and SSS
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Proving Two Triangles Similar with Shortcuts
• Instead of using the definition of similarity to prove that two triangles are congruent (all corresponding angles are congruent and all corresponding sides are proportional), you can use three shortcuts:– Angle-Angle (AA)– Side-Angle-Side (SAS)– Side-Side-Side (SSS)
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Angle-Angle (AA) Similarity Postulate
• If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
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AA Example
Explain why the triangles are similar and write a similarity statement.
∠R ≅ ∠V (Given)
∠RSW ≅ ∠VSB (vertical angles are congruent)
ΔRSW ≅ ΔVSB (AA)
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Side-Angle-Side (SAS) Similarity Theorem
• 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 triangles are similar.
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CB
A
H
J
G
ΔABC ~ ΔGJH
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SAS Example
Explain why the two triangles are similar and write a similarity statement.
∠Q ≅ ∠X since they are right angles
The two sides that include the right angles are proportional
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By SAS, ΔPRQ ~ΔZYX
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Side-Side-Side (SSS) Similarity Theorem
• If the corresponding sides of two triangles are proportional, then the triangles are similar.
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CB
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ΔABC ~ ΔGJH
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SSS Example
Explain why the two triangles are similar and write the similarity statement.
Since all sides of the two triangles are proportional, by SSS, ΔABC ~ ΔEFG
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EF
AB
GF
CB
EG
AC