5-7: Pythagorean Theorem and PPTs
Learning Targets:

Simplify expressions involving square roots

Use the Pythagorean Theorem to find missing side lengths

Determine if a given set of side lengths form a Pythagorean Triple
*************Simplifying Square Root Expressions***********************************
The First 20 Perfect Squares
12 = 1
62 = 36
112 = 121
162 = 256
22 = 4
72 = 49
122 = 144
172 = 289
32 = 9
82 = 64
132 = 169
182 = 324
42 = 16
92 = 81
142 = 196
192 = 361
52 = 25
102 = 100
152 = 225
202 = 400
**To simplify a square root, factor the greatest perfect square factor and take the square root
Example 1: Simplify each square root expression.
a)
√112
b) √180
c) √294
d) 5√1734
***************************The Pythagorean Theorem****************************
∆𝐴𝐵𝐶 shown below is a right ∆ ↔ 𝑎2 + 𝑏 2 = 𝑐 2 .
A

a, b are the lengths of the legs
opposite the acute ∠𝑠

c is the length of the
hypotenuse
c
b
C
B
a
Example 2: Find the missing side lengths. Give answers in simplest radical form.
a)
12
15
15
b)
8
10
F
Example 3: Wes drives 19 miles east, 2 miles north, 5 miles east, and then travels 5 more miles north
before arriving at his destination. How far did he travel from his starting point “as the crow flies”?
******************************Pythagorean Triples******************************
A Pythagorean Triple is a set of 3 nonzero whole numbers a, b, and c such that 𝑎2 + 𝑏 2 = 𝑐 2 .
** (3, 4, 5) form a Pythagorean Triple since 32 + 42 = 52
** 12 + 2.42 = 2.62 , but (1, 2.4, 2.6) do not form a Pythagorean triple. Why?
16
Example 3: Find the missing side lengths. Then tell if the lengths form a Pythagorean Triple.
a)
b)
9
30
16
F
7
5-7: Pythagorean Theorem and PPTs
Learning Targets:

Simplify expressions involving square roots

Use the Pythagorean Theorem to find missing side lengths

Determine if a given set of side lengths form a Pythagorean Triple
*************Simplifying Square Root Expressions***********************************
The First 20 Perfect Squares
12 = 1
62 = 36
112 = 121
162 =
22 = 4
72 = 49
122 = 144
172 =
32 = 9
82 = 64
132 =
182 =
42 = 16
92 = 81
142 =
192 =
52 = 25
102 = 100
152 =
202 =
**To simplify a square root, factor the greatest perfect square factor and take the square root
Example 1: Simplify each square root expression.
a)
√112
b) √180
c) √294
d) 5√1734
***************************The Pythagorean Theorem****************************
∆𝐴𝐵𝐶 shown below is a right ∆ ↔ 𝑎2 + 𝑏 2 = 𝑐 2 .
A

a, b are the lengths of the legs
the acute ∠𝑠

c is the length of the hypotenuse
c
b
C
B
a
Example 2: Find the missing side lengths. Give answers in simplest radical form.
a)
12
15
15
b)
8
10
F
opposite
Example 3: Wes drives 19 miles east, 2 miles north, 5 miles east, and then travels 5 more miles north
before arriving at his destination. How far did he travel from his starting point “as the crow flies”?
******************************Pythagorean Triples******************************
a, b, and c such that 𝑎2 +
A Pythagorean Triple is a set of 3 nonzero whole numbers
𝑏2 = 𝑐 2.
** (3, 4, 5) form a Pythagorean Triple since 32 + 42 = 52 and 3, 4, and 5 are all whole numbers.
** 12 + 2.42 = 2.62 , but (1, 2.4, 2.6) do not form a Pythagorean triple. Why?
16
Example 3: Find the missing side lengths. Then tell if the lengths form a Pythagorean Triple.
a)
b)
9
30
16
F
7
( 3 , 4 , 5 ) ( 5, 12, 13) ( 7, 24, 25) ( 8, 15, 17) ( 9, 40, 41) (11, 60, 61) (12, 35, 37) (13, 84, 85) (16, 63, 65)
(20, 21, 29)