Overhead Sheets
Pythagorean
Theorem
1
Pythagorean Theorem
Review:
A right triangle is triangle with a
right angle. The legs of a right
triangle are the two sides that form
the right angle. The hypotenuse of
a right triangle is the longest side,
the side opposite the right angle.
Leg
Hypotenuse
L
Leg
2
In any right triangle with leg
lengths a and b and hypotenuse
lengths c, a2 + b2 = c2
If the side lengths of any triangle
satisfy the equation a2 + b2 = c2,
then the triangle is a right triangle,
and c is its hypotenuse.
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TAKS Grade 8
A right triangle is shown below.
Which set of numbers represents the lengths
of the sides of a right triangle?
A 12, 4, 14,
B 5, 3, 4,
C 6, 8, 11
D 2, 9, 8
4
TAKS Grade 8
Which figure best represents a triangle with
sides a, b, and c in which the relationship
a2 + b2 = c2 is always true?
5
TAKS Grade 8
Mr. Elliott designed a flower garden in the
shape of a square. He plans to build a
walkway through the garden, as shown
below.
Which is closest to the length of the walkway?
A
B
C
D
36 ft.
24 ft.
17 ft.
13 ft.
6
TAKS Grade 9
In a town, there is a small garden shaped like
a triangle, as shown below. The side of the
garden that faces Sixth Street is 80 feet in
length. The side of the garden that faces
Third Avenue is 30 feet in length.
What is the approximate length of the side of
the garden that faces Elm Street?
F
G
H
J
35 ft
40 ft
85 ft
100 ft
7
TAKS Grade 9
A square park has a diagonal walkway from
one corner to another. If the walkway is
about 38 yards long, what is the approximate
length of each side of the park?
A
B
C
D
6 yd
19 yd
27 yd
54 yd
8
TAKS Grade 10
The drawing shows part of the plan for a new
underground lawn-sprinkler system.
Plan for sprinkler system
Which is closest to the length of the section of
plastic pipe from point A to point C?
A
B
C
D
4.7 ft
5.7 ft
6.7 ft
7.7 ft
9
TAKS Grade 10
Mrs. Cheung hired a landscaping service to plant
a row of bushes around her triangular backyard.
If the bushes must be planted 3 feet apart,
approximately how many bushes are needed
for Mrs. Cheung’s backyard?
A
B
C
D
23
25
28
32
10
TAKS Grade 11
A wooden pole was broken during a
windstorm. Before it broke, the total height
of the pole above the ground was 25 feet.
After it broke, the top of the pole touched the
ground 15 feet from the base.
How tall was the part of the pole that was left
standing?
F
G
H
J
8 ft
10 ft
17 ft
20 ft
11
TAKS Grade 11
Kim walked diagonally across a rectangular
field that measured 100 feet by 240 feet.
Which expression could be used to determine
how far Kim walked?
12
Pythagorean Triples
Any set of 3 whole numbers that satisfy the
Pythagorean Theorem is called a
Pythagorean triple. The set of numbers
{5, 12, 13} forms a Pythagorean triple
because these numbers satisfy the
Pythagorean Theorem.
a2 + b2 = c2
Does 52 + 122 = 132?
25 + 144 = 169
169 = 169
Yes. Therefore {5, 12, 13} is a Pythagorean
Triple.
Is {7, 9, 12} a Pythagorean Triple?
13