GSP c8SIMILAR polygons'gsp

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..\..\Geo Misc\vanishing point.gsp

• GSP c8\SIMILAR polygons.gsp

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Similar Triangles and Polygons
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Similarity

• Two figures with the same shape are said to be
  similar.
• The symbol is used to denote similarity.
• The corresponding vertices of similar polygons
  are congruent angles.
• Labeling is critical

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Similarity

• Labeling is critical
• ?ABC ?DEF
• ?A? ?D
• ?B? ?E
• ?C? ?F
• quadrilateral WXYZ ABCD

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Similarity
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Similarity
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Similarity

• Similarity Demo in GSP

GSP c8\sim_JW.gsp
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Vanishing Point
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Vanishing Point
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Definition

• Definition Two polygons are similar if and only
  if two conditions are satisfied
• All pairs of corresponding angles are congruent.
• All pairs of corresponding sides are proportional.

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Postulate

• Postulate If three angles of one triangle are
  congruent to three angles of a second triangle,
  then the triangles are similar. (AAA)

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Corollary

• Corollary If two angles of one triangle are
  congruent to two angles of another triangle, then
  the triangles are similar. (AA)
• Why is it necessary to only have two congruent
  angles to have similar triangles?

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CSSTP

• CSSTP Corresponding sides of similar triangle
  are proportional.

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Example

• 1.8.2  Quadrilateral EFGH is similar to
  quadrilateral RSTU. Find the value of y.
• A.114 B.71  C.95 D.80

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Example

• 2.8.2  The statement two parallelograms are
  similar is_______. 
• A. true if and only if the parallelograms are
  rectangles
• B. sometimes true 
• C. never true
• D. always true

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Example

• 3.8.2  Which word can be inserted in the sentence
  to make a true statement? All_______ are
  similar. 
• A. Triangles
• B. Rectangles 
• C. Rhombi
• D. squares 

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Example

• 4.8.2.  Trapezoid ABCD trapezoid EBFG. Find
  AD.   
• A.7
• B.10 
• C.28
• D.12

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Example

• 5.8.2  The two polygons shown are similar. Find
  the value of x.   
• A. 5/3
• B. 20/3
• C. 16/5
• D. 3/5

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Example

• 1.8.3  Find the value of x in the figure.   
• A. 6.0
• B. 5.4 
• C. 3.2
• D. 3.6

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Example

• 2.8.3  The two triangles shown are similar by
  ______.   
• A. SAS Similarity
• B. ASA Similarity 
• C. AA Similarity
• D. SSS Similarity

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Example

• 3. 8.3  Which one of the triangles shown is not
  similar to the others?   
• A.Z
• B.Y 
• C.X
• D.W

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Example

• 4. 8.3  Find the value of x.
• A.5
• B.12.5 
• C.7.5
• D.4.5

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Example

• 5.8.3  What is a property that similarity of
  triangles does not have? 
• A. Symmetric
• B. commutative 
• C. Transitive
• D. reflexive

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8.2.3
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8.2.4
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8.2.5
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8.2.9
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8.2.10
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8.2.14
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8.3.9 Prove ?PTA?PBT
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8.3.10
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8.3.20
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What is similar about these?Oh, also what are
they?