LESSON
The Pythagorean Theorem
5-7
Lesson Objectives (p. 348):
______________________________________________________________
______________________________________________________________
Vocabulary
1. Pythagorean triple (p. 349): _______________________________________
______________________________________________________________
Key Concepts
2. Theorem 5-7-1—Converse of the Pythagorean Theorem (p. 350):
THEOREM
HYPOTHESIS
CONCLUSION
5-7-1
3. Theorem 5-7-2—Pythagorean Inequalities Theorem (p. 351):
Theorem 5-7-2
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
113
Geometry
LESSON
The Pythagorean Theorem
5-7
Lesson Objectives (p. 348):
use the Pythagorean Theorem and its converse to solve problems; use
______________________________________________________________
Pythagorean inequalities to classify triangles.
______________________________________________________________
Vocabulary
set of three nonzero whole numbers a, b, and
1. Pythagorean triple (p. 349): a
_______________________________________
c______________________________________________________________
such that a 2 b 2 c 2.
Key Concepts
2. Theorem 5-7-1—Converse of the Pythagorean Theorem (p. 350):
THEOREM
HYPOTHESIS
5-7-1 If the sum of the
squares of the
lengths of two sides
of a triangle is equal
to the square of the
length of the third
side, then the
triangle is a right
triangle.
CONCLUSION
ABC is a right
triangle.
B
c
A
a
C
b
a2 b2 c 2
3. Theorem 5-7-2—Pythagorean Inequalities Theorem (p. 351):
Theorem 5-7-2
In ABC, c is the length of the longest side.
If c 2 a 2 b 2, then ABC is
an obtuse triangle.
If c 2 a 2 b 2, then ABC is an
acute triangle.
B
B
c
c
a
a
A
b
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
C
A
113
b
C
Geometry
LESSON 5-7 CONTINUED
4. Get Organized In each box, summarize the Pythagorean relationship.
(p. 352).
Pythagorean
Relationships
Pythagorean Theorem:
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Converse of the
Pythagorean Theorem:
114
Pythagorean Inequalities Theorem:
Geometry
LESSON 5-7 CONTINUED
4. Get Organized In each box, summarize the Pythagorean relationship.
(p. 352).
Pythagorean
Relationships
Pythagorean Theorem:
In a right , the sum of the
squares of the leg lengths
equals the square of
the hypotenuse.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Converse of the
Pythagorean Theorem:
If the sum of the squares of 2
side lengths of a equals the
square of the third side length,
then the is a right .
114
Pythagorean Inequalities Theorem:
In a with c as the length of
the longest side, if c2 > a2 + b2,
the is obtuse, but if
c2 < a2 + b2, the is acute.
Geometry