Pythagorean Theorem

20
Pythagorean Theorem Solving Right Triangles

Transcript of Pythagorean Theorem

Page 1: Pythagorean Theorem

Pythagorean TheoremSolving Right Triangles

Page 2: Pythagorean Theorem

Solving Right Triangles Directions

As you view this presentation, take notes and work out the practice problems.

When you get to the practice problem screens, complete the step in your notebook before continuing to the next slide.

Page 3: Pythagorean Theorem

The Right Triangle

• A right triangle has one 90o

angle, A 90o angle is also called a right angle. You know which angle is the right angle because it will have a box at the angle.

• The side across from the right angle is called the hypotenuse and is usually labeled with the letter c,

• The other two sides are called legs and are usually labeled with the letters a and b.

ca

b

Page 4: Pythagorean Theorem

Pythagorean Theorem

• The mathematician Pythagoras proved the relationship between the sides of a right triangle and the hypotenuse. This relationship is known as the Pythagorean Theorem

c

b

a

Page 5: Pythagorean Theorem

Finding the Hypotenuse of a Right Triangle

Practice Problem 1

Step 1: Substitute the values of a and b into a2 +b2 = c2.

c = ?

b = 5

a = 12

Page 6: Pythagorean Theorem

Finding the Hypotenuse of a Right Triangle

Practice Problem 1

Step 1: Substitute the values of a and b into a2 +b2 = c2.

c = ?

b = 5

a = 12122 +52 = c2

Page 7: Pythagorean Theorem

Finding the Hypotenuse of a Right Triangle

Practice Problem 1

Step 1: 122 + 52 = c2

c = ?

b = 5

a = 12

Step 2: Do the math.

Page 8: Pythagorean Theorem

Finding the Hypotenuse of a Right Triangle

Practice Problem 1

Step 1: 122 + 52 = c2

c = 13

b = 5

a = 12

Step 2: Do the math.

Page 9: Pythagorean Theorem

Finding the Hypotenuse of a Right Triangle

Practice Problem 2

Step 1: Substitute the values of a and b into a2 +b2 = c2.

c = ?

b = 5

a = 6

Page 10: Pythagorean Theorem

Finding the Hypotenuse of a Right Triangle

Practice Problem 2

Step 1: Substitute the values of a and b into a2 +b2 = c2.

c = ?

b = 5

a = 662 + 52 = c2

Page 11: Pythagorean Theorem

Finding the Hypotenuse of a Right Triangle

Practice Problem 2

Step 1: 62 + 52 = c2

c = ?

b = 5

a = 6

Step 2: Do the math.

Page 12: Pythagorean Theorem

Finding the Hypotenuse of a Right Triangle

Practice Problem 2

Step 1: 62 + 52 = c2

b = 5

a = 6

Step 2: Do the math.Note: c2 is not always a perfect square. Always read directions carefully to know what form your answer should take.

Page 13: Pythagorean Theorem

Finding a Leg of a Right TrianglePractice Problem 1

Step 1: Substitute the values of a and c into a2 +b2 = c2.

c = 10b = 8

a = ?

Page 14: Pythagorean Theorem

Finding a Leg of a Right TrianglePractice Problem 1

Step 1: Substitute the values of a and c into a2 +b2 = c2.

c = 10b = 8

a = ?

a2 + 82 = 102

Page 15: Pythagorean Theorem

Finding a Leg of a Right TrianglePractice Problem 1

Step 1: Substitute the values of a and c into a2 +b2 = c2.

c = 10b = 8

a = ?

a2 + 82 = 102

Step 2: Do the math.

Page 16: Pythagorean Theorem

Finding a Leg of a Right TrianglePractice Problem 1

Step 1: Substitute the values of a and c into a2 +b2 = c2.

c = 10b = 8

a = 6

a2 + 82 = 102

Step 2: Do the math.

a2 + 64 = 100

a2 = 36

a = 6

Page 17: Pythagorean Theorem

Finding a Leg of a Right TrianglePractice Problem 2

Step 1: Substitute the values of b and c into a2 + b2 = c2.

c = 9b = ?

a = 5

Page 18: Pythagorean Theorem

Finding a Leg of a Right TrianglePractice Problem 2

Step 1: Substitute the values of b and c into a2 + b2 = c2.

c = 9 b = ?

a = 5

52 + b2 = 92

Page 19: Pythagorean Theorem

Finding a Leg of a Right TrianglePractice Problem 2

Step 1: 52 + b2 = 92.

c = 9 b = ?

a = 5

Step 2: Do the math.

Page 20: Pythagorean Theorem

Finding a Leg of a Right TrianglePractice Problem 2

Step 1: 52 + b2 = 92.

c = 9

a = 5

Step 2: Do the math.

Note: You should always simplify the square root if possible.