I can use the Pythagorean Theorem to find missing legs and the
hypotenuse of right triangles and solve practical problems.
4.1
Page#
sum
PYTHAGOREAN THEOREM : a theorem that says in any right triangle, the _________
of the
squares of the legs is equal to the square of the hypotenuse.
•
shorter
LEGS (of a right triangle) – the two _________________
sides that form the right angle
•
longest
HYPOTENUSE (of a right triangle) – the ____________________
side, across from the
right angle.
The Pythagorean Theorem
a2
+
b2
=
c2
Leg #1
(a or b)
Hy
po
te
nu
se
(c
)
Leg #2
(a or b)
legs
hypotenuse
Where “a” and “b” are the ___________,
and “c” is the ________________.
Finding the hypotenuse (c)
c2 (plug numbers into theorem)
32 + ______
42 = ______
______
leg
2
leg2
hypotenuse2
c2
16
______
= ______
(simplify)
9 + ______
x
2
25 = ______
c
______
(add)
3 ft
25 = ______
c (take the square root of both sides)
______
2
4 ft
5
c
______
= ______
Finding A MISSING SIDE (a or b)
2
a
12
20 (plug numbers into theorem)
______
+ ______
= ______
2
2
2
2
leg
leg
2
hypotenuse
a2
144 = ______
400 (simplify)
______ + ______
20 ft
144 (subtract ______
144 from both sides)
-______
2
a
256
______
= ______
2
a
256 (take the square root of both sides)
______
= ______
12 ft
a = ______
16
______
© Asia Hines 2021
x
144
- ______
4.1
Name ____________________
Date _____________________
PYTHAGOREAN THEOREM PRACTICE
Directions: Use the Pythagorean Theorem to find the missing leg (side) below! Round to the nearest
tenth, when needed.
1.
5.
x
3
12
x
11
4
32 + 42 = x2
x=5
2.
6.
x
5
112 + x2 = 122
x = 4.8
20
10
x
12
52 + 122 = x2
x = 13
6
3.
102 + x2 = 202
x = 17.3
7.
x
15
6
17
x
8
62 + 82 = x2
x = 10
4.
A ladder is leaned up against a wall. The bottom of the ladder
is 8 feet from the wall. The top of the ladder reaches a spot on
the wall that is 15 feet off the ground. How long is the ladder?
82 + 152 = x2
17 = x
152 + x2 = 172
x=8
8. If a 14-meter long ramp is put at a dock that is 3 meters high,
how far is the bottom of the ramp from the dock?
32 + x2 = 142
x = 13.7
©Asia Hines 2021
I can determine whether a triangle is a right triangle, given the
measures of its three sides and prove the Pythagorean Theorem.
4.2
Page#
IS IT A RIGHT TRIANGLE?
To determine if three side lengths form a right triangle, plug them into the Pythagorean
hypotenuse
c
Theorem! Use the longest side as your ________________________,
“ _______.”
Let’s try it out!
1)
3)
6, 8, 10
9, 12, 18
62 + 82 = 102
36 + 64 = 100
100 = 100
92 + 122 = 182
81 + 144 = 324
225 ≠ 324
Yes or No
2)
Yes or No
4)
10, 24, 26
16, 30, 34
102 + 242 = 262
100 + 576 = 676
676 = 676
162 + 302 = 342
256 + 900 = 1156
1156 = 1156
Yes or No
Yes or No
PYTHAGOREAN TRIPLES
are sets of three positive integers that could be the lengths of a right triangle,
that is, they satisfy a2 + b2 = c2.
3
4
5
8
15
17
6
8
10
10
24
26
5
12
13
9
12
15
7
24
25
12
16
20
© Asia Hines 2021
-
I can determine whether a triangle is a right triangle, given the
measures of its three sides and prove the Pythagorean Theorem.
4.2
Page#
What is the area of
this square?
9
3
9 + 16 = 25
25 = 25
5
4
What is the area of
this square?
What is the area of
this square?
25
16
1. What is the area of the other square?
2. What is the area of the other square?
25 ft2
25 + 144 = c
169 = c
64 + b = 100
b = 36
© Asia Hines 2021
144 ft2
4.2
Name ____________________
Date _____________________
PYTHAGOREAN THEOREM PRACTICE
Directions: Determine if the following sets of numbers form a right triangle.
1.
5.
6.4, 12, 12.2
2.1, 7.2, 7.5
Yes
6.42 + 122 = 12.22
184.96 ≠ 148.84
2.
3.
Yes
no
7.
Yes
or
no
or
no
5, 12, 13
Yes
52 + 122 = 132
169 = 169
or
or
no
8, 5, 11
Yes
82 + 52 = 112
89 ≠ 121
or
no
8. Find the area of the other square.
7, 10, 12.2
72 + 102 = 12.22
149 ≠ 148.84
2.12 + 7.22 = 7.52
56.25 = 52.25
6.
3.6, 6.5, 7.4
3.62 + 6.52 = 7.42
55.21 ≠ 54.76
4.
no
6, 8, 9
62 + 82 = 9 2
100 ≠ 81
6
or
Yes
Yes
169 ft2
or
no
a + 144 = 169
a = 25ft2
25
ft2
2 2
144
144ftft
©Asia Hines 2021