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Family Patterns in Right Triangles: A Quick Guide

Explore families of right triangles like {3, 4, 5} and {5, 12, 13} to simplify triangle problems. Find the GCF to determine the family a triangle belongs to and solve for missing sides using Pythagorean Theorem.

lesley-levy
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Family Patterns in Right Triangles: A Quick Guide

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  1. Families of Right Triangles

  2. Look for a pattern in these triangles. • Triangles B, C, D are multiples of triangle A • This is called the {3, 4, 5} family • There are infinite members of this family.

  3. Other common families that will help you by saving time • {5, 12, 13} • {7, 24, 25} • (8, 15, 17} • There are infinitely many more families but these are the most common

  4. Which family does this triangle belong to? • Look for the greatest common factor of both given sides. • GCF = 2, divide this out of both sides. • This triangle belongs to {5, 12, 13} • Missing side is 13(2) = 26

  5. Which family does this triangle belong to? • This is a {3, 4, 5} that has been divided by 2 • So the missing side is

  6. Which family does this belong to?

  7. What family does this belong to?

  8. All of these can still be solved using the Pythagorean Theorem if you do not recognize a family. • The idea of families is to make your life easier not harder.

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