Area postulate

Algebra

The triangle angle sum theorem

Algebra

Angle addition theorem

Area of a square

Algebra

Definition

Algebra

SAS (Side-Angle-Side)

CPCTC

Algebra

Algebra

Definition

<B = <D = <C = <A = 90

Triangle JBK = Triangle KCL = Triangle LDM = Triangle 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