Pythagorean Theorem
Pythagorean theorem worksheet #1-9 homework Pythagorean theorem worksheet #1-9
What is a right triangle? hypotenuse leg right angle leg It is a triangle which has an angle that is 90 degrees. The two sides that make up the right angle are called legs. The side opposite the right angle is the hypotenuse.
The Pythagorean Theorem: A tool for right triangle problems only When do I need to use the Pythagorean Theorem? When I know: length of 2 sides and need to know: length of 3rd side
What is the Pythagorean Theorem? c a b Where a and b are legs and c is the hypotenuse
A Pythagorean Puzzle Draw a square on each side.
A Pythagorean Puzzle Measure the length of each side c b a
A Pythagorean Puzzle Work out the area of each square. C² c b b² a a²
A Pythagorean Puzzle c² b² a²
A Pythagorean Puzzle
A Pythagorean Puzzle 1
A Pythagorean Puzzle 1 2
A Pythagorean Puzzle 1 2
A Pythagorean Puzzle 1 2 3
A Pythagorean Puzzle 1 2 3
A Pythagorean Puzzle 1 3 2 4
A Pythagorean Puzzle 1 3 2 4
A Pythagorean Puzzle 1 3 2 5 4
A Pythagorean Puzzle 1 What does this tell you about the areas of the three squares? 3 2 5 4 The red square and the yellow square together cover the green square exactly. The square on the longest side is equal in area to the sum of the squares on the other two sides.
A Pythagorean Puzzle Put the pieces back where they came from. 1 3 5 2 4
A Pythagorean Puzzle Put the pieces back where they came from. 1 3 2 5 4
A Pythagorean Puzzle Put the pieces back where they came from. 1 3 2 5 4
A Pythagorean Puzzle Put the pieces back where they came from. 1 2 5 4 3
A Pythagorean Puzzle Put the pieces back where they came from. 1 5 4 2 3
A Pythagorean Puzzle Put the pieces back where they came from. 5 4 2 3 1
A Pythagorean Puzzle c²=a²+b² c² b² This is called Pythagoras’ Theorem. a²
Find the length of the missing leg. 4 cm 10 cm 42 + b2 = 102 16 + b2 = 100 -16 -16 b2 = 84 The leg is about 9.2 cm long.
Find the length of the missing leg. a2 + 122 = 132 a2 + 144 = 169 -144 -144 a2 = 25 The leg is 5 inches long.
Find the length of the hypotenuse if a = 12 and b = 16. 122 + 162 = c2 144 + 256 = c2 400 = c2 Take the square root of both sides. 20 = c
Find the length of the hypotenuse if a = 5 and b = 7. 52 + 72 = c2 25 + 49 = c2 74 = c2 Take the square root of both sides. 8.60 = c
Find the length of the hypotenuse given a = 6 and b = 12 180 324 13.42 18
42 + b2 = 102 16 + b2 = 100 Solve for b. 16 - 16 + b2 = 100 - 16 Find the length of the leg, to the nearest hundredth, ifa = 4 and c = 10. 42 + b2 = 102 16 + b2 = 100 Solve for b. 16 - 16 + b2 = 100 - 16 b2 = 84 b = 9.17
a2 + 72 = 102 a2 + 49 = 100 Solve for a. a2 = 100 - 49 a2 = 51 Find the length of the leg, to the nearest hundredth, if 4. c = 10 and b = 7. a2 + 72 = 102 a2 + 49 = 100 Solve for a. a2 = 100 - 49 a2 = 51 a = 7.14
Find the length of the missing side given a = 4 and c = 5 1 3 6.4 9
Tim rode 8 miles due north, then 3 miles due east Tim rode 8 miles due north, then 3 miles due east. How far, to the nearest mile, is Tim from where he started? 3 Draw a picture: 8 x
Remember: How am I suppose to leave my answer? Solve the problem a2 + b2 = c2 82 + 32 = c2 64 + 9 = c2 73 = c2 Remember: How am I suppose to leave my answer? C = 8.5440037 Tim is 9 miles from where he started.