chapter six review by mitch, andrew, gwyne, pietro
TRANSCRIPT
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Chapter Six Review
By Mitch, Andrew, Gwyne, Pietro
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6.1 Similar Polygons
Vocabularysimilar: shapes with congruent corresponding angles and proportional corresponding sides
scale factor: the ratio of the lengths between corresponding sides (2:5, 6:13, 1:3)
TheoremsSimilar 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
Vocabularydilation: transformation with same angle measures and proportional corresponding sides from original to imagescale 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~ PostulateIf 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 ProportionalityTheoremIf lines 1 and 2 areparallel, then
Side Splitter TheoremIf BD is and angle bisector of<ABC, then a/x=b/y or
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6.6 Similarity Transformations
Vocabularycenter of dilation: the fixed point around which a figure is enlarged or reduced (dilated)enlargement: if k>1 in (kx, ky)reduction: if 0<k<1 in (kx, ky)
(It's kind of a boring chapter, people)
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Quiz!
Small Triangle: a=10, b=6, c=9Large Triangle: a=27, b=16.2, c=24.3
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~ Theoremb) Yes, by SAS~ Theoremc) Yes, by AAA~ Theoremd) No, not similare) Yes, by AAS~ Theoremf)None of the above
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8. Another name for a dilation is a...a) Changeb) Shrinkc) Similarity transformationd) 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.