advertisement

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*

*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

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**