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Properties of Equality and Congruence

Logical rules that allow equations to be manipulated and solved.

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Properties Of Equality And Congruence
Teacher Contributed

RWA Properties of Equality and Congruence


Mixed Martial Arts


  • Transitive property fallacy
  • Transitive property

Student Exploration

“Simply stated, the Transitive Property Fallacy of MMA is this: if Fighter A beats Fighter B, and Fighter B beats Fighter C, then Fighter A would beat Fighter C. This works in math, or so people who went to school past the ninth grade tell me (personally, I never had a use that much schoolin’), but it doesn’t work in MMA (mixed martial arts) for several different reasons.”

Read more here...


photo from The Fighting Life


Extension Investigation

Have students give other examples of the transitive property fallacy.

Layering (optional)

Properties of Equality - http://www.basic-mathematics.com/properties-of-equality.html

Write a two column algebraic proof using the properties of equality. See an example here:

Have students turn their proof into a paragraph proof. See an example here: http://www.homeschoolmath.net/teaching/two-column-proof.php/

Use the properties or equality to solve a real world situation. See an example here: http://www.floridastandards.org/Standards/PublicPreviewBenchmark593.aspx

Write your solution as a two column algebraic proof.

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