# Lesson 1

### Triangle Review

A

scalene

triangle has no sides and no angles equal.

An

isosceles

triangle has two sides and two angles equal.

An

equilateral

triangle has three sides and three angles equal.

A

right

triangle has one right angle.

Identify the triangle below;

right isosceles

How are the three sides of a right triangle related to each other?

a

### The Pythagorean Theorem

a

2

+ b

2

= c

2

c

Hypotenuse

, the longest side of a right triangle

b

c

2

= a

2

+ b

2 c

2

= 8

2

+ 6

2 c

2

= 64 + 36 c

2 c

= 100

100 c = 10

8

6 c

x

x

12

hypotenuse

7 a

2

+ b

2

x

2

+ 7

2

= c

2

= 12

2

x

2

x

2

x

2 x

+ 49 = 144

= 144

= 95

95

x

= 9.7

### Similar Triangles

Two triangles are considered to be similar if and only if:

• they have the same shape

• corresponding angles are equal

• the ratio of the corresponding side lengths are equal

Ex 1. Find x.

F

C

1 m

A

72 cm

B D

18.5 m x

E

Step 1: Identify two similar triangles.

ABC ~

DEF

Step 2: Write equivalent ratios

AB

DE

BC

EF

AC

DF

Step 4: Use the ratios that apply to solve for x.

AB

DE

BC

EF

0 .

72

18 .

5

1

x

0.72

x

= 18.5

0 .

72

x

0 .

72

18 .

5

0 .

72

x

= 25.7 m

C

1 m

A

72 cm

B D

18.5 m

F

E x

Ex #2: Surveyors have laid out triangles to find the length of a lake.

Calculate this length, AB.

Step 1: Draw a labeled diagram.

PROVIDED

Step 2: Identify two similar triangles.

ACB ~

ECD

Step 3: Write equivalent ratios

AC

EC

CB

CD

AB

ED

ft ft ft

Step 4: Use the ratios that apply to solve for x.

CB

CD

AB

ED

208

24

x

30

24

x

( 30 )( 208 )

24

x

6240

24

24

x

6240

24

x

260

ft

ft ft ft