NAME:___________________________
Math______,Period____________
Mr.Rogove
Date:__________
Learning Objective:WewillprovethePythagoreantheoremusing
similartriangles.(G8M7L9)
Concept Development:
WecanusesimilartrianglestoprovideanotherproofofthePythagoreanTheorem:
Namethesethreetriangles
Arethesethreetrianglessimilar?
ProvingthePythagoreanTheorem:
1
G8M7L9:MoreproofsofthePythagoreanTheorem
NAME:___________________________
Math______,Period____________
Mr.Rogove
Date:__________
AnotherProofusingSimilarTrianglesandAreas
2
G8M7L9:MoreproofsofthePythagoreanTheorem
NAME:___________________________
Math______,Period____________
Mr.Rogove
Date:__________
Guided Practice:
StepsforProvingthePythagoreanTheoremUsingSimilarTriangles
1.Drawalinefromtherightangleperpendiculartothehypotenuse.Thiswillcreate
threesimilartriangles.
2.Label,reorient,anddrawthethreesimilartriangles.
3.Setupaseriesofproportionstoshowthat!! + ! ! = ! ! usingthesteps
demonstratedonthefirstpageofthenotes.
15
9
12
3
G8M7L9:MoreproofsofthePythagoreanTheorem
NAME:___________________________
Math______,Period____________
Mr.Rogove
Date:__________
4
25
15
20
G8M7L9:MoreproofsofthePythagoreanTheorem
NAME:___________________________
Math______,Period____________
Mr.Rogove
Date:__________
Independent Practice:
Noindependentpractice…
Activating Prior Knowledge:
WeknowthePythagoreanTheoremis!! + ! ! = ! ! ANDweknowonewaytoprove
it.
a
b
a
c
b
c
c
a
b
c
b
a
Closure:
Whyarethethreetrianglescreatedduringtheproofsimilar?
Notes:
MapstoGrade8,Lesson15,Module7.
HWcouldbelesson15problemsetminusprobs1-2.
5
G8M7L9:MoreproofsofthePythagoreanTheorem