The triangle angle sum theorem

CPCTC

Algebra

Definition

Area of a square

SAS (Side-Angle-Side)

Algebra

Algebra

Algebra

Angle addition theorem

Definition

Algebra

Algebra

Area postulate

∠B = ∠D = ∠C = ∠A = 90

△JBK = △KCL = △LDM = △MAJ

KJ = LK = ML = JM (label them h)

∠X + ∠Y + ∠B = 180

∠X + ∠Y = 90

∠X + ∠Y + ∠1 = 180

∠1 = 90 (repeat for angles 2, 3 and 4)

KLMJ is a square

Area of ADCB = (f + g)^2

Area of ADCB = area of the four triangles + area of KLMJ

Area of ADCB = 2fg + h^2

(f+g)^2 = 2fg + h^2

f^2 + 2fg + g^2 = 2fg + h^2

f^2 + g^2 = h^2