Transcript 8-1: The Pythagorean Theorem and its Converse

8-1: The Pythagorean
Theorem and its Converse
Learning Goal: Use the Pythagorean Theorem
to calculate the length of the side of a right
triangle or determine if a triangle is right.
The Pythagorean Theorem ONLY
works on RIGHT triangles!
EX: A 15 ft ladder is leaning against a
building. It reaches a window that is 9 ft
off the ground. How far from the
building is the base of the ladder?
You try!
A ramp is built to make a building
wheelchair assessable. The ramp begins
24 ft from the building and rises to a
vertical height of 7 ft. How long is the
ramp?
Will the sides always be whole numbers?
NO!
 Pythagorean Triples – 3 whole numbers
that satisfy the Pythagorean Theorem (no
decimals or fractions)
 Shortcut for Pythagorean Theorem!
 Most common ones are
3 – 4 – 5
 5 – 12 – 13
 7 – 24 – 25
 8 – 15 – 17
EX: Do the sides form a Pythagorean
Triple?
The legs of a right triangle have lengths
10 and 24. what is the length of the
hypotenuse? (If you can draw a picture
to represent the problem, you don’t
have to write the words!)
EX: What is the height of the seesaw? Express
answer in simplest radical form AND round to
the nearest inch.
The Converse to the Pythagorean
Theorem
 If a2 + b2 = c2  right triangle
 If a2 + b2 > c2  acute triangle
 If a2 + b2 < c2  obtuse triangle
EX: Given the 3 side lengths, is each
triangle right, acute, or obtuse?
A) 85, 84, 13
B) 6, 11, 14
8-1 Assignment: Due Tuesday by the
end of class.
Workbook pg 203 # 2 – 26
Turn in to the bin by the end of class
Tuesday.