Thursday, March 5, 2009

Problem 265: Right Triangle, Pythagorean Theorem

Proposed Problem
Problem 265. Right Triangle, Pythagorean Theorem.

See complete Problem 265 at:

Level: High School, SAT Prep, College geometry

1 comment:

  1. See the drawing

    Define a square ABCD
    Define E in AB, AE=a and EB=b
    Define F in BC such as BF=b and FC=a

    Cut [AEIH] in 2 triangles T1=AEI and T2=AHI
    Cut [FCGI] in 2 triangles T3=FCG and T4=FIG
    AEI, AHI, FCG and FIG are congruent with surface T=ab/2
    Define c=AI=FG


    Translate T2 such as HI becomes DG
    Translate T1 such as EI becomes BF
    Translate T4 such AS GI becomes A’A
    By symetry, A’F’FG is a square => [A’F’FG]=c^2
    [ABCD] =4T+[A’F’FG] =4T+c^2
    But [ABCD]=a^2+b^2+4T
    Therefore a^2+b^2=c^2