Objective to solve problems involving the pythagorean theorem
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Objective- To solve problems involving the Pythagorean Theorem. For Right Triangles Only!. - always opposite the right angle. hypotenuse. leg. leg. Objective- To solve problems involving the Pythagorean Theorem. For Right Triangles Only!. hypotenuse. c. a. leg. b. leg.

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Objective to solve problems involving the pythagorean theorem
Objective- To solve problems involving the Pythagorean Theorem.

For Right Triangles Only!

- always opposite

the right angle

hypotenuse

leg

leg


Objective to solve problems involving the pythagorean theorem1
Objective- To solve problems involving the Pythagorean Theorem.

For Right Triangles Only!

hypotenuse

c

a

leg

b

leg


Objective to solve problems involving the pythagorean theorem2
Objective- To solve problems involving the Pythagorean Theorem.

For Right Triangles Only!

hypotenuse

c

a

b

a

b


Objective to solve problems involving the pythagorean theorem3
Objective- To solve problems involving the Pythagorean Theorem.

For Right Triangles Only!

Pythagorean Theorem

c

a

b


Solve for x. Theorem.

x

6

8


Solve for y. Theorem.

7

4

y


Solve for t. Theorem.

6

t

15


Pythagorean triples
Pythagorean Triples Theorem.

3 4 5

6 8 10

9 12 15

12 16 20


Pythagorean triples1
Pythagorean Triples Theorem.

3 4 5

5 12 13

7 24 25

6 8 10

10 24 26

14 48 50

9 12 15

15 36 39

21 72 75

12 16 20

12

9

15


To the nearest tenth of a foot, find the length Theorem.

of the diagonal of a rectangle with a width of

4 feet and a length of 10 feet.

x

4 ft.

10 ft.


A car drives 20 miles due east and then 45 miles Theorem.

due south. To the nearest hundredth of a mile,

how far is the car from its starting point?

20 miles

x

45 miles


Informal proof 1
Informal Proof #1 Theorem.

Inscribe a square within the square.


Informal proof 11
Informal Proof #1 Theorem.

a

b

c

a

b

c

c

b

c

a

b

a


Informal proof 12

a Theorem.

Informal Proof #1

b

c

a

b

c

a

b

c

c

b

c

a

b

a


Informal proof 13

a Theorem.

Informal Proof #1

b

c

b

c

a

c

b

c

a

b

a


Informal proof 14

a Theorem.

Informal Proof #1

b

c

b

c

b

c

a

a

c

b

c

a

b

a


Informal proof 15

a Theorem.

Informal Proof #1

b

c

b

c

b

c

a

a

c

a

b


Informal proof 16

a Theorem.

Informal Proof #1

b

c

b

c

b

c

a

a

b

c

a

c

a

b


Informal proof 17

a Theorem.

Informal Proof #1

b

c

c

b

a

b

c

a

c

a

b


Informal proof 18

a Theorem.

Informal Proof #1

b

c

c

b

a

b

c

a

c

a

c

a

b

b


Informal proof 19

a Theorem.

Informal Proof #1

b

c

c

b

a

b

c

a

c

a

b


Informal proof 110

a Theorem.

Informal Proof #1

b

c

c

b

a

b

c

a

c

a

b


Informal proof 111

a Theorem.

Informal Proof #1

b

c

a

c

b

b

c

a

b

c

a

c

a

b


Informal proof 112
Informal Proof #1 Theorem.

a

c

b

b

c

a

c

b

b

a

c

a

c

a

b


Informal proof 113
Informal Proof #1 Theorem.

a

b

c

c

b

b

a

c

a

c

a

c

a

b

b


Informal proof 114
Informal Proof #1 Theorem.

a

b

c

c

b

b

a

b

c

a

c

a

c

a

b


Informal proof 115
Informal Proof #1 Theorem.

a

b

c

c

b

a

b

c

a

c

a

b


Informal proof 2
Informal Proof #2 Theorem.

a + b

-

Total Purple Yellow

Area Area Area

=

a

b

-

=

c

a

b

c

c

b

c

a

b

a


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