- no [Diff: 1]
- [Diff: 2]
- inches[Diff: 2]
- [Diff: 2]
- squaremillimeters[Diff: 3]
- squarefeet [Diff: 3]
- squareyards[Diff: 3]
11.Proof. The plan is, we will find the area of the greensquarein two ways.Sincethosetwo areasmust
be equal,we can set thoseareasequalto eachother.
For the innersquare(in green),we can directlycomputethe area:.
Now, the area of the large,outersquareis. Don’tforgetto multiplythis binomialcarefully!
The area of eachsmallright triangle(in yellow)is
.
Sincethereare four of thoseright triangles,we havethe combinedarea
Finally, subtractthe area of the four yellowtrianglesfrom the area of the largersquare,and we are left with
Puttingtogetherthe two differentwaysfor findingthe area of the innersquare,we have
Converseof the PythagoreanTheorem
LearningObjectives
- Understandthe converseof the PythagoreanTheorem.