11-4 PYTHAGOREAN
THEOREM AND ITS
CONVERSE
SWBAT
• Use the Pythagorean Theorem
The Pythagorean Theorem
A Little about the Pythagorean Theorem
• Named for the Greek Mathematician Pythagoras around
6th Century B.C.
• Theorem was well known before Pythagoras was named
for it by the ancient Babylonians, Egyptians and Chinese.
Example 1a: Pythagorean Theorem
Find AB
Example 1b: Pythagorean Theorem
A triangle has a
hypotenuse of 25 and a
leg of 10.
• What is the length of
the other Leg in
simplest radical form?
• What is the decimal
equivalent (round to
two decimal places).
Example 2a: Simplest Radical Form
Find the value of x.
Leave your answer in
simplest radical form.
Ex 2b: Simplest Radical Form
Simplest Radical form or Decimals?
• Why use one over the other?
• We use decimals to answer general real world questions.
• Radicals are the most exact answer. (No Rounding)
• Simplest Radical form is used when there is an exact
mathematical answer is needed.
Ex 3a: Real World
• Trig is going to across a lake in
order to reach his Feline Greenies
cat treats.
• How far would Trig have to swim
from Dock to Dock? If necessary,
round to the nearest whole
number.
Ex 3b: Real World
• A baseball diamond is a square with 90ft sides.
• How far is it from Home Plate to Second Base? If
necessary, round to the nearest hundredth.
• Try these. Find each missing side. Give answers in both
simplest radical form and a decimal approximation to the
nearest tenth (if necessary).
a)
b)