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ALGEBRA – LESSON 97
Pythagorean Theorem
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Pythagorean Theorem
We know that if you add up the 3 angles of a
triangle, they will always add up to:
180o
In any triangle, if two angles are congruent,
then the sides opposite those angles are also
congruent
Pythagorean Theorem
In a right
triangle, the
longest side is
called the:
hypotenuse
We will always
designate the
hypotenuse with the
letter c. The two
shorter sides will
always be a or b.
c
a
b
Pythagorean
Theorem:
a2 + b2 = c 2
Pythagorean Theorem
We will use the theorem we learned yesterday to
solve these, with one “common sense” note.
Because the length of a side can never be a
negative number, we know that the square root of
any number will be positive for these answers.
Solve for x.
Pythagorean
Theorem:
a2 + b2 = c 2
282 + 282 = x2
1568 = x2
39.6 = x
#1
Pythagorean Theorem
Solve for x.
Pythagorean
Theorem:
a2 + b2 = c 2
302 + 162 = x2
1156 = x2
34 = x
#2
Pythagorean Theorem
Some right triangles are known as Pythagorean
triples because the sides are all whole numbers.
You need to memorize:
3-4-5
5-12-13
6-8-10
10-24-26
9-12-15
15-36-39
7-24-25
8-15-17
We also know that any multiple of a Pythagorean
triple is also a Pythagorean triple.
Pythagorean Theorem
Recall the appropriate Pythagorean triple to find
the unknown length in each of the following.
a = 15
#3
Pythagorean Theorem
Recall the appropriate Pythagorean triple to find
the unknown length in each of the following.
b=5
#3
Pythagorean Theorem
Recall the appropriate Pythagorean triple to find
the unknown length in each of the following.
c=6
#3
Pythagorean Theorem
Recall the appropriate Pythagorean triple to find
the unknown length in each of the following.
a = 12
#4
Pythagorean Theorem
Recall the appropriate Pythagorean triple to find
the unknown length in each of the following.
b = 12
#4
Pythagorean Theorem
Recall the appropriate Pythagorean triple to find
the unknown length in each of the following.
c = 25
#4
Homework: Problem Set 97