Section 8.3 Proving Triangles Similar

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Section 8.3Proving Triangles Similar

• By Asad Ashraf

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What is Similarity

• Similar figures are figures in which the shape is
  exactly the same, but the size is not.
• A Dilation is an enlargement of a figure. It is
  still similar, however.
• A Reduction is a reduction of a figure. This is
  also similar.
• Remember that similar figures are not
  necessarily congruent

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Proving Triangles Similar

• There are several methods to prove triangles
  similar.
• These are very similar to the methods of proving
  triangles congruent.
• The methods are AAA, AA, SAS, and SSS.

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AAA Postulate

• AAA  Postulate  - If three angles of one
  triangle are congruent to three angles of a 2nd
  triangle then the triangles are similar.

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AA Theorem

• AA if 2 angles of one triangle are congruent
  to two angles of a 2nd triangle then the
  triangles are similar.
• This is proved by the No-Choice Theorem and AAA
  Theorem combined.

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SSS Theorem

• SSS If 3 sides of one triangle are proportional
  to three sides of a 2nd triangle then the two
  triangles are similar.

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SAS Theorem

• SAS   If two sides of one triangle are
  proportional to the corresponding two sides of a
  2nd triangle and their included angles are
  congruent, then the triangles are similar.

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Sample Problems

• Click Here
• SSS and SAS Problems

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Sample Problems
Are these triangles ?
Answer Yes they are because Included angles
were given congruent and the ratios of the sides
are congruent as well.
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Practice Problems

• Prove that an acute angle of one right angle is
  congruent to the vertex angle of an isosceles
  triangle, they are similar.
• Always, Sometimes, Never
• If 2 triangles are similar, they are congruent
  ____
• If 2 triangles are congruent, they are similar
  ____
• 2 rectangles are similar if neither is a square
  ____
• 2 right triangles are similar____

Answers A, S, S, S
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Practice Problems

• Are any 2 isosceles triangles similar? Show all
  work.

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Practice Problems

• Are these triangles similar? Why or why not?

Answer NO
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Practice Problems

• Given XS and RY are Altitudes of RTS
• Prove Triangle TSX is similar to Triangle TYR

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Works Cited

• Our Book
• Similar Triangles. Mathwarehouse.com. May
  27,2008.lthttp//www.mathwarehouse.com/geometry/sim
  ilar/triangles/index.htmlgt.
• Chapter 8. Teacherweb.org. 2003. May
  27,2008.lthttp//teacherweb.ftl.pinecrest.edu/wingj
  oa/My20Webs/Geometry/chpt8.htmTest20Review20-
  2020Chapter208.1-4gt.