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
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