9.1 The Pythagorean Theorem
Pythagorean Theorem: ___________________________________________
Find the value of x.
1)
2)
12
x
x
24
3)
7
4√3
4
5
x
12
4)
8
x
5) A rectangle has a length 2.4 and width 1.8. Find the length of a diagonal.
6) A rectangle has a diagonal of 2 and length of √3 . Find its width.
Write the Pythagorean Theorem as an if/then statement.
Converse of the Pythagorean Theorem:
Determine if the given measures are measures of the sides of a right triangle.
Most Common Triples
Pythagorean Triple:
11) a. Complete the Pythagorean triple table.
b. These Pythagorean triples are called a family. Why to you think this is?
c. Are the triangles described by a family of Pythagorean triples
similar? Explain.
12) For each Pythagorean triple, find two triples in the same family.
a) 8, 15, 17
b) 9, 40, 41
c) 7, 24, 25
Find the value of x. Then tell whether the side lengths form a
Pythagorean triple.
13)
14)
Pythagorean Inequalities
In triangle ABC with longest side c:
If ______________________________, then triangle ABC is acute.
If _______________________________, then triangle ABC is right.
If _______________________________, then triangle ABC is obtuse.
Classify each triangle as acute, right, or obtuse.
15)
17)
16)
18)
Find the value of x. Then tell whether the side lengths form a
Pythagorean triple.
13)
14)
Pythagorean Inequalities
In triangle ABC with longest side c:
If ______________________________, then triangle ABC is acute.
If _______________________________, then triangle ABC is right.
If _______________________________, then triangle ABC is obtuse.
Classify each triangle as acute, right, or obtuse.
15)
17)
16)
18) 16, 30, 36
19) Determine whether ∆JKL with vertices J(-2,2), K(-1,6), and L(3,5) is
a right triangle. Show your work.
20)
21)
IXL-like Problems