Chapter Six Review

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Chapter Six Review

• By Mitch, Andrew, 
• Gwyne, Pietro

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6.1 Similar Polygons

• Vocabulary
• similar shapes with congruent corresponding
  angles and proportional corresponding sides
• scale factor the ratio of the lengths between
  corresponding sides (25, 613, 13)
• Theorems
• Similar Polygon Perimeters
•      If two polygons are similar, the ratio of
  their perimeters is the same as the ratio of the
  lengths of their corresponding sides

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6.2 Transformations and Dilations

• Vocabulary
• dilation transformation with same angle measures
  and proportional corresponding sides from
  original to image
• scale factor also called k, number coordinates
  are multiplied for image- (kx, ky) 
• -If you move a figure onto another figure with a
  dilation, then the figures are similar
• -You can also combine dilations with
•  reflections, translations, and rotations!

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6.3 Triangles Similar by AA Postulate

• AA Postulate
• If two angles of one triangle are congruent to
  two angles of a different triangle, the triangles
  are similar.

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6.4  Triangles Similar SSS, SAS

• SSS Theorem
•     If the corresponding sides of two triangles
  are proportional, then the triangles are similar.
• SAS Theorem
•     If two corresponding sides of a triangle are
  proportional and the included angles are
  congruent, then the triangles are similar.

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6.5 Use Proportionality Theorems

• Triangle Proportionality
• Theorem
• If lines 1 and 2 are
• parallel, then 
• Side Splitter Theorem
• If BD is and angle bisector of
• ltABC, then a/xb/y or
•  

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6.6 Similarity Transformations

• Vocabulary
• center of dilation the fixed point around which
  a figure is enlarged or reduced (dilated)
• enlargement if kgt1 in (kx, ky)
• reduction if 0ltklt1 in (kx, ky)
•                
•                         (It's kind of a boring
  chapter, people)

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Quiz!

• Small Triangle a10, b6, c9
• Large Triangle a27, b16.2, c24.3
• 1.Are the triangles similar?  If so, what is the
  scale factor from the small triangle to the large
  triangle? 

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2.  What are the transformations of the triangles?

•  

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3.  Are the triangles similar? By what
theorem/postulate?

•  

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4. Prove the triangles similar using SSS or SAS

•  

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5. Find x.

•                                               
                   Find x.

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6. Draw a figure with the given vertices using a
scale factor of .5.  Is the dilation a reduction
or an enlargement?

• S(-4,2)
• U(-2,4)
• P(2,4)
• E(4,2)
• R(0,-3)
•  

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Multiple Choice 

• 7.  Are the triangles similar?
• a) Yes, by AA Theorem
• b) Yes, by SAS Theorem
• c) Yes, by AAA Theorem
• d) No, not similar
• e) Yes, by AAS Theorem
• f)None of the above

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• 8.  Another name for a dilation is a...
• a)  Change
• b) Shrink
• c) Similarity transformation
• d) Glenn

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Always, Sometimes, Never? 

• 9. A rotation is a form of dilation.
• 10.  Similar triangles are congruent. 
• 12.  Isosceles triangles are similar.