## RWA Properties of Equality and Congruence

### Topic

Mixed Martial Arts

### Vocabulary

- 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...

http://thefightinglife.wordpress.com/2008/03/13/the-transitive-property-fallacy/

photo from The Fighting Life

http://thefightinglife.wordpress.com/2008/03/13/the-transitive-property-fallacy/

### 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.