Chapter Six Review

By Mitch, Andrew, Gwyne, Pietro

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

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!

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.

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.

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 

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)

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? 

2.  What are the transformations of the triangles?

 

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

 

4. Prove the triangles similar using SSS~ or SAS~ 

5. Find x.

                                                                Find x.

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) 

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

8.  Another name for a dilation is a...a)  Changeb) Shrinkc) Similarity transformationd) Glenn

Always, Sometimes, Never? 

9. A rotation is a form of dilation.

10.  Similar triangles are congruent. 

12.  Isosceles triangles are similar.