Pythagorean Triples

1
Pythagorean Triples

• Objective To determine missing measures by
  finding and using Pythagorean Triples

2
Pythagorean Triples

• These are simply numbers which fit the rule
  ________________________

a2 b2 c2
3
Pythagorean Primitives
Know by ? !

• The lengths of the sides of the four
  triangles shown below are examples of Pythagorean
  Triples which are called,__________. These three
  numbers have _________________________.

3-4-5 8-15-17 5-12-13
7-24-25
primitives
no common integer factors.
4
L k
for one of the Pythagorean primitives to save
yourself a lot of work in solving the following
problems!
Know by ? !
3-4-5 8-15-17 5-12-13
7-24-25
1. a _____ 2. Area __________ 3.
Perimeter ?
5
MultiplesComplete the table below
Primitives Doubles Triples 4 times 10 times
__ __ __
__ __ __
8 __ __
7 24 __

• 4 5 6-8-10 9-12-15 12-16-20
  30-40-50
• 5 12 13 10-24-26 15-36-39 20-48-53
  50-120-130
• 15 17 16-30-34 24-45-51 32-60-68
  80-150-170
• 25 14-48-50

? ? ?
6
Application Multiples

• Recognize multiples of Pythagorean
  
• Triples to speed up the process of
• finding missing measurements. All
  
• units are in centimeters.

NOTE You will need the lengths of two sides to
begin!
d 15 e 8
f 25
7
Final Checks for Understanding

• Define Pythagorean triples, then name the
  primitives.
• Explain how using the primitives and their
  multiples can speed up the process of determining
  missing measures in right triangles.

8
Final Checks.

• Use your Pythagorean primitives (or their
  multiples) to determine missing measures in the
  right triangles below

24 cm
A _____ 7cm
9cm 15 cm
_____ Find the
perimeter. _____ ___




9
Homework Assignment

• Primitives and their Multiples WS plus textbook
  problems _______________