9.2 The Pythagorean Theorem

Report
7.1-2 The Pythagorean Theorem
Mrs. Wilkins
Geometry
Objectives/Assignment
•Prove the Pythagorean Theorem
•Use the Pythagorean Theorem to solve
real-life problems such as determining how
far a ladder will reach.
History Lesson
•Around the __ century BC, the Greek
mathematician Pythagorus founded a school for
the study of _____, mathematics and science.
Many people believe that an early ___ of the
Pythagorean Theorem came from this school.
•Today, the ___________ is one of the
most famous theorems in geometry. Over ___
different proofs now exist.
Theorem 9.4: Pythagorean Theorem
•In a _____
triangle, the square
of the length of the
hypotenuse is equal to
the ___ of the
squares of the legs.
c
a
b
a2 + b2 = c2
Ex. 1: Finding the length of the hypotenuse.
•Find the value of x.
12
5
x
Ex. 2: Finding the length of the leg.
•Find the value of x.
15
x
26
Ex. 3: Finding the length of the leg.
•Find the value of x.
Ex. 4 Finding the length of the hypotenuse.
•Find the value of x.
x
19
8
Is the triangle acute, obtuse or right?
RIGHT
ACUTE
OBTUSE
Ex. 5 Classify the triangles given their side lengths
• 10, 11, 14
• 6, 8, 10
• 12, 16, 20
• 4, 7, 9
• 5, 6, 7
• 15, 36, 39
7.1-2 The Pythagorean Theorem
Mrs. Wilkins
Geometry
Find the unknown side length
x
18
12
Find the unknown side length
x
4
√5
Find the unknown side length
x
x
2√5
Find the unknown side length
20
12
x
Using the Pythagorean Theorem
•A Pythagorean triple is a set of _____
positive integers a, b, and c that satisfy the
equation _________. For example, the
integers 3, 4 and 5 form a Pythagorean
Triple because 32 + 42= 52.
Pythagorean Triples
3,4, 5
5, 12, 13
8, 15, 17
7, 24, 25
The given lengths are two sides of a right triangle. The sides
together form a Pythagorean triple. Find the length of the third
side and tell whether it is a leg or the hypotenuse.
•24 and 51
•20 and 25
•72 and 75
Pythagorean Triples
3,4, 5
5, 12, 13
6, 8, 10
15, 36, 39
8, 15, 17
7, 24, 25
Classify the triangles given their side lengths
14, 25, 30
55, 7, 10
31,15, 16

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