The Pythagorean Theorem

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Presentation transcript:

The Pythagorean Theorem Right Triangles ONLY

Remember the formula? c a Legs Hypotenuse b

1. Finding the hypotenuse a2 + b2 = c2 152 + 202 = c2 225 + 400 = c2 625 = c2 20 15 x

2. Finding a side a2 + b2 = c2 62 + b2 = 102 36 + b2 = 100 -36 -36 b2 = 64 b = 8 10 6 x

3. See if the triangle is a right triangle 5 4 a2 + b2 = c2 32 + 42 = 52 9 + 16 = 25 25 = 25 3 Yes we have a right triangle.

The ladder reaches 14 feet up the wall. 4. A 15 foot ladder leans up against a building. the foot of the ladder is 5 feet from the base of the building. How high up the wall, to the nearest foot does the ladder reach? a2 + b2 = c2 x2 + 52 = 152 x2 + 25 = 225 - 25 -25 x2 = 200 X = √200 x = 10√2 x 15 5 The ladder reaches 14 feet up the wall.

Tim is 9 miles from where he started. Tim rode 8 miles due north, then 3 miles due east. How far, to the nearest mile, is Tim from where he started? 3 a2 + b2 = c2 82 + 32 = c2 64 + 9 = c2 73 = c2 √73 = C =c 8 x Tim is 9 miles from where he started.

Remember the properties of a rhombus: The diagonals of a rhombus are 6 cm and 8 cm. What is the length of each side of the rhombus? Remember the properties of a rhombus: The diagonals of a rhombus bisect each other The diagonals of a rhombus are perpendicular The sides of a rhombus are congruent

3 4 a2 + b2 = c2 32 + 42 = c2 9 + 16 = c2 25 = c2 √25 = c 5 = c x 4 3 A rhombus is really 4 right triangles in disguise! Each side of the rhombus measures 5 cm.

Need more help? Watch these videos https://www.youtube.com/watch?v=bolqc5qMkrg https://www.youtube.com/watch?v=4bWjyA-j1sI