Unit 6 Part 1

Using Proportions,Similar Polygons,

and Ratios

Different ways to write ratios.

Of course as a fraction. 2/3

2:3

2 to 3

Algebra Example

3x – 1 7

4 8

24x – 8 = 28

. +8 +8

24x = 36

24 24 x = 1.5 or 3:2

=

Another Example

x + 12 3x + 4

8 4

Answer is …

x = .8 or 4:5

=

4x + 48 = 24x + 32

Similar Triangles are Proportional.

Triangles with proportional sides are similar triangles. (Note: the corresponding angles are then congruent)

Example

Find the missing side of the similar triangles below.

3

9

5n n = 15

Word Problem

You are planning to paint a mural on a rectangular wall. You know that the perimeter of the wall is 482 feet and that the ratio of its length to its width is 9:2 . Find the area of the wall.Here is what you know L:W = 9:2 2L +2W = P P = 482 9:2 = 9x:2x

2(9x) + 2(2x) = 484

x = 22

L = 9(22) = 198

W = 2(22) = 44

area = 198(44) = 8712 ft²

Word Problem

The measure of the angles in triangle CDE have a ratio of 1:2:3. Find the measures of the angles.

Solution is …

1x + 2x + 3x = 180º

x = 30º

C = 30º , D = 60º , E = 90º

AB : BC = 3:8

Find the value of k.

k:20 = 3:8

k = 7.5

A

BC

k

20

Example

Are the ratios equal?

2 12

3 , 18

If the geometric extreme equals the geometric mean, then the ratios are equal. Or If the two ratios reduce to the same ratio, then they are equal.

Similar Polygons

Scale FactorThe scale factor is simply the ratio which when multiplied by the side it equals the corresponding side of the other figure.

Find the scale ratio of the triangles below.

3 5

Let x = the scale factor, then