Chapter 7 – Similarity

Ratio – a ratio is a quotient of two numbers, or a fraction; a comparison of two quantities by division

It represents the rate at which one thing compares to another.

Since it is a fraction, it should always be in simplest form.

7-1 Ratios

Can be written three ways◦ , a:b, or a to b

Example: In standard definition TV’s (old TV’s), the ratio of the width:height is 4:3 (4/3); on newer HDTV’s, the ratio is 16:9 (16/9).

Ratios

16:4 = 4:1 (4/1 or 4 to 1)

6:9 = 2:3 (2/3 or 2 to 3)

25:75 = 1:3 (1/3 or 1 to 3)

Simplify the following ratios

We can state a ratio of parts within a figure: ∠ABC:∠ACB = ∠A:∠AED = AD:DE = (AC+BC):AE =

7-1 Ratio

We can state a ratio of parts within a figure: ∠ABC:∠ACB = 40:120 = 1:3 (1/3) ∠A:∠AED = 20:120 = 1:6 (1/6) AD:DE = 16:6 = 8:3 (8/3) AC+BC:AE = 5+3:10 = 8:10 = 4:5 (4/5)

7-1 Ratio

When indicating the ratio between two measurement, we never want a decimal involved:

A sheet of printer paper is 8.5 by 11 inches. What is the ratio of the length to the width?

11:8.5 ⁂ But, we don’t want decimals, so what should we do?

Ratio = _____

7-1 Ratio

Ratios can be made from more than 2 measures:

A triangle that has angle measures 30-60-90 would have a ratio of 1:2:3 among its 3 sides.

A triangles with sides 3, 12, and 9 would have a ratio of 1:4:3.

7-1 Extended Ratio

If we know that the ratio among the angles of a triangle is 2:3:4, what are the angle measures?

7-1 Using Ratios to find Measures

If we know that the ratio among the angles of a triangle is 1:12:5, what are the angle measures?

7-1 Using Ratios to find Measures

If we know that one angle of a triangle is 45° and the ratio among the other angles of the triangle is 2:1, what are the remaining angle measures?

7-1 Using Ratios to find Measures

Proportions A proportion is an equation that states two

or more ratios are equal

Example: a:b = c:d

7-1 Proportions

Using that Ratio, we know a few things:

a:b = c:d a ∙ d = b ∙ c b and c are called the means a and d are called the extremes

7-1 Proportions

Properties of Proportions

a c b db d ad = bc a c

a b a+b c+dc d b d

a = c = e then a = c = e = a+c+eb d f b d f b+d+f

Applying those properties:

2 = 63 9

2:3 = 6:9 2 ∙ 9 = 3 ∙ 6

7-1 Proportions

That last property allows us to solve proportions:

100n = 3000 n = 30

7-1 Proportions

That last property allows us to solve proportions:

75n = 1800 n = 24

7-1 Proportions

7-1worksheet #1-17 all 7-2 worksheet #1-7 and 18-20 all

Homework