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
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 = 100 c

100 c = 10
8
6 c

x
x
12 hypotenuse
7 a 2 + b 2 = c 2 x 2 + 7 2 = 12 2 x 2 + 49 = 144 x 2 = 144
x 2 = 95 x

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
 x
24 30
24 x

( 30 )( 208 )
24 x

6240
24
24 x

6240
24 x

260 ft ft ft ft