Similar Polygons - Commack Schools

112b CN Similar polygons.notebook

1

Polygons are similar (~) when:

1.) All corresponding angles are congruent and

2.) All corresponding sides are proportional.

Similar Polygons

Polygon: a simple closed figure made up of 3 or more line segments

Polygons that have the same shape are called similar polygons.

The symbol used to represent similar polygons is ~Congruent same measure. The symbol for congruent is

Polygon ABCD Polygon WXYZThe parts of similar polygons that "match" are called "corresponding" parts. There are corresponding angles and corresponding sides.

Corresponding angles (<)

<A corresponds to <W

<B corresponds to <X

<C corresponds to <Y

<D corresponds to <Z

Corresponding sides

AB corresponds to WX

BC corresponds to XY

CD corresponds to YZ

DA corresponds to ZW

You read this as: Angle A You read this as: line segment AB

https://www.youtube.com/watch?v=8hBeLqfa3E https://www.youtube.com/watch?v=Tlq9amS9hy4


2

You read this as: Angle A is congruent to Angle X

To determine if the corresponding line segments are proportional, you need to set up ratios. The numerator and denominator of each ratio are the measurements of the corresponding sides. Be consistent in how you set up your ratios. The results of each of the ratios must be equal.

Note: the numerators are the line segments from the triangle on the left and the denominators are the line segments from the triangle on the right you need to be consistent when setting up your ratios.


3

Determine whether rectangle HJKL is similar to rectangle MNPQ. Explain your reasoning.

Steps:

1) Check to see if corresponding angles are congruent.

2) Prove if corresponding sides are proportional or not.

3) Write your answer in a sentence. Be specific with your wording.

Step 1:

Since the two polygons are rectangles, all their angles are right angles 900 each. Therefore, all corresponding angles are congruent (have the same measure.)

As you can see,1/2 is not equal to 7/10. Therefore the corresponding sides to the rectangles are not proportional.

Step 2:

Now set up a ratio representing each of the four corresponding sides of the rectangle. Reminder be consistent in how the ratios are set up.

Step 3:

Corresponding angles are congruent but corresponding sides are not proportional. Therefore, rectangle HJKL is NOT similar to rectangle MNPQ.


4

All angles of a rectangle are equal to 900 (right angles). Therefore, all corresponding angles are congruent

Determine whether the polygons are similar. Explain your reasoning.

Suggestion: You may want to redraw one of the rectangles so they are facing the same direction. This will help when setting up your ratios.

Ratios:

Since the ratios are not equal, corresponding sides are not proportional.

Corresponding angles are congruent but corresponding sides are not proportional. Therefore, these rectangles are not similar.


5

Determine whether each pair of polygons are similar.

5.

6.

A

B

C E

F

G

As you can see, corresponding angles are congruent.

Ratios:

Corresponding angles are congruent but correspondent sides are not proportional. Therefore, these triangles are not similar figures.


13.5

6

6 7.5

Corresponding angles are congruent.

Ratios:

Corresponding sides are proportional since all ratios are equal.

Corresponding angles are congruent and corresponding sides are proportional. Therefore, these trapezoids are similar figures.


15 12

18


Ratios:

Corresponding sides are proportional since all ratios are equal.

Corresponding angles are congruent and corresponding sides are proportional. Therefore, these triangles are similar figures.

All angles of a rectangle are equal to 900 (right angles). Therefore, all corresponding angles are congruent

Ratios:



Corresponding angles are congruent but correspondent sides are not proportional. Therefore, these rectangles are not similar figures.



6

Find the missing side(s) of these SIMILAR figures.Steps:

You need to set up a proportion.

1) set up one ratio with the side that is missing to the corresponding side on the other figure.

2) set that ratio equal to one other ratio representing corresponding sides.

3) Solve your proportion either using cross products or equivalent ratios.

To solve for m:

proportion:

Now solve for n otherwise know as AB.

n

18

Proportion:

Now solve for p otherwise know as WZ.

p16

18

Proportion:


7

The triangles below are SIMILAR. Write a proportion to find its missing measure x.

Proportion:

As you can see, it does not matter which corresponding sides you pick as the other ratio in your proportion. You will get the same answer.


8

a)

b)

c)

d)

Proportion:

Suggestion: redraw the smaller triangle to face the same direction as the larger triangle.

equivalent ratios

3

x

Proportion:

Suggestion: redraw the smaller rectangle to face the same direction as the larger rectangle.

Proportion:

Proportion:

8

4.84

Suggestion: redraw the smaller triangle to face the same direction as the larger triangle.


9

Questions 58: Solve for the missing side x.

Questions 14.


10

corresponding sides are proportional. corresponding sides are not proportional.

corresponding sides are proportional. corresponding sides are proportional.

Rectangle

100 101

Rectangle

74

10

8

10

15

12

3.53

3.5

1.5

3.63.9

Questions 14.

Questions 58: Solve for x.


11

Hint: convert meters into centimeters first.


12

Note: 8 inches is the width, 10 inches is the length

Perimeter: Add up all the sides


13

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Similar Polygons - Commack Schools