Triangle Review

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?

The Pythagorean Theorem

a

b

c

a2 + b2 = c2

Hypotenuse, the longest side of a right triangle

8

6

c

Example 1: Calculate side c.

c2 = 82 + 62 c2 = 64 + 36 c2 = 100c 100=c = 10

c2 = a2 + b2

x2 + 49 = 144

x2 = 95x 95=x = 9.7

Example 2: Calculate side x.

12

7x a2 + b2 = c2

x2 + 72 = 122

x2 = 144 – 49 hypotenuse

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

Step 1: Identify two similar triangles.

A B

C

D E

F

72 cm

1 m

18.5 m

x

ABC ~ DEF

Step 2: Write equivalent ratios

DF

AC

EF

BC

DE

AB==

Ex 1. Find x.

72 cm

1 m

18.5 m

x

A B

C

D E

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

EF

BC

DE

AB=

x

1

5.18

72.0=

0.72x = 18.5

x = 25.7 m

72.0

5.18

72.0

72.0=

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.

Step 2: Identify two similar triangles.

ACB ~ ECD

Step 3: Write equivalent ratios

ED

AB

CD

CB

EC

AC==

PROVIDED

ft

ft

ft

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

ED

AB

CD

CB=

3024

208 x=

)208)(30(24 =x

624024 =x

24

6240

24

24=

x

ftx 260=

ft

ft

ft