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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. Triangle Review. A right triangle has one right angle. Identify the triangle below;. right isosceles. - PowerPoint PPT Presentation
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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
