Transcript Pythagorean_Theorem_Examples.ppt

The Pythagorean Theorem and Its Converse
Lesson 8-1
Geometry
Additional Examples
A right triangle has legs of length 16 and 30. Find
the length of the hypotenuse. Do the lengths of the sides
form a Pythagorean triple?
a2 + b2 = c2
Use the Pythagorean Theorem.
162 + 302 = c2
Substitute 16 for a and 30 for b.
256 + 900 = c2
Simplify.
1156 = c2
34 = c
Take the square root.
The length of the hypotenuse is 34.
The lengths of the sides, 16, 30, and 34, form a Pythagorean triple
because they are whole numbers that satisfy a2 + b2 = c2. Notice
that each length is twice the common Pythagorean triple of 8, 15,
and 17.
The Pythagorean Theorem and Its Converse
Lesson 8-1
Geometry
Additional Examples
Find the value of x. Leave your answer in simplest radical
form.
a2 + b2 = c2
Use the Pythagorean Theorem.
x2 + 102 = 122
Substitute x for a, 10 for b, and 12 for c.
x2 + 100 = 144
Simplify.
x2 = 44
Subtract 100 from each side.
x =
Take the square root of each side.
x =2
4(11)
11
Simplify.
The Pythagorean Theorem and Its Converse
Lesson 8-1
Geometry
Additional Examples
A baseball diamond is a square with 90-ft sides. Home plate
and second base are at opposite vertices of the square. About how far
is home plate from second base?
Use the information to draw a baseball diamond.
a2 + b2 = c2
902 + 902 = c2
8,100 + 8,100 = c2
Use the Pythagorean Theorem.
Substitute 90 for a and for b.
Simplify.
16,200 = c2
c=
c
16,200
Take the square root.
127.27922 Use a calculator.
The distance to home plate from second base is about 127 ft.
The Pythagorean Theorem and Its Converse
Lesson 8-1
Geometry
Additional Examples
Is this triangle a right triangle?
a2 + b2
c2
42 + 62
72
16 + 36
49
Substitute 4 for a, 6 for b, and 7 for c.
Simplify.
52 ≠ 49
Because a2 + b2 ≠ c2, the triangle is not a right triangle.
The Pythagorean Theorem and Its Converse
Lesson 8-1
Geometry
Additional Examples
The numbers represent the lengths of the sides of a
triangle. Classify each triangle as acute, obtuse, or right.
a.15, 20, 25
c2
a2 + b2
Compare c2 with a2 + b2.
252
152 + 202
Substitute the greatest length for c.
625
225 + 400
Simplify.
625 = 625
Because c2 = a2 + b2, the triangle is a right triangle.
The Pythagorean Theorem and Its Converse
Lesson 8-1
Geometry
Additional Examples
(Continued)
b. 10, 15, 20
c2
a2 + b 2
Compare c 2 with a2 + b 2.
202
102 + 152
400
100 + 225
400
325
Because c2
Substitute the greatest length for c.
Simplify.
a2 + b2, the triangle is obtuse.