Chapter 7 Lesson Chapter 7 Lesson 2: Similar 2: Similar PolygonsPolygons

Geometry CPGeometry CP

Mrs. MongoldMrs. Mongold

Similar PolygonsSimilar Polygons

Definition: Polygons that have Definition: Polygons that have exactly the same shape but not exactly the same shape but not necessarily the same size.necessarily the same size.

Symbol for SimilaritySymbol for Similarity

The symbol used in statements for The symbol used in statements for similarity is the tildasimilarity is the tilda

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Steps to determine Steps to determine similaritysimilarity

1. Make sure the polygons are the same 1. Make sure the polygons are the same shape, both triangles, quadrilaterals, shape, both triangles, quadrilaterals, pentagons, etc and all angles are congruent.pentagons, etc and all angles are congruent.

2. Match up corresponding sides, the 2. Match up corresponding sides, the longest sides are a pair, the shortest sides longest sides are a pair, the shortest sides are a pair, and everything in between.are a pair, and everything in between.

3. Write scale factors in simplest form for 3. Write scale factors in simplest form for EVERY pair of corresponding sides.EVERY pair of corresponding sides.

4. Determine similarity, if all scale factors 4. Determine similarity, if all scale factors are equal then the shapes are similar, if one are equal then the shapes are similar, if one is different they are not!is different they are not!

Practice ProblemPractice Problem

Determine if the figures are similar Determine if the figures are similar or not.or not.

104

4

5

5

3

8 8

10

6

Follow the StepsFollow the Steps

1. Are they the same shape?1. Are they the same shape? Yes, PentagonsYes, Pentagons

2. Match up the sides.2. Match up the sides. 10 with 5, 8 with 4, and 6 with 310 with 5, 8 with 4, and 6 with 3

3.Write scale factors in simplest form.3.Write scale factors in simplest form. 10/5 = 2, 8/4 = 2, and 6/3 = 210/5 = 2, 8/4 = 2, and 6/3 = 2

4. Determine similarity.4. Determine similarity. The pentagons are similar because all scale The pentagons are similar because all scale

factors are equalfactors are equal

More Practice on pg 14 More Practice on pg 14 and 15and 15

Pg 14Pg 14 1. Yes similar, SF 1. Yes similar, SF

5/85/8 2. No not similar 2. No not similar

because the angles because the angles are not the sameare not the same

3. Yes similar, SF 3. Yes similar, SF ½½

4.Yes similar, SF 4.Yes similar, SF 5/45/4

Pg 15Pg 15 1. SF 2/3, x = 6, y 1. SF 2/3, x = 6, y

= 15= 15 2. SF 2/1, x = 2.25, 2. SF 2/1, x = 2.25,

y = 5y = 5 3. SF 2/3, x = 27, y 3. SF 2/3, x = 27, y

= 15= 15 4. SF 4/3, x = 24, y 4. SF 4/3, x = 24, y

= 27= 27

Homework Due Homework Due TomorrowTomorrow

Pages 16 and 17 (skip #5 on pg 17)Pages 16 and 17 (skip #5 on pg 17)