Pythagoras Theorem — Formula Sheet

l(PR)^2 = l(PQ)^2 + l(QR)^2

q^2 = p^2 + r^2

AC^2 = AB^2 + BC^2

[(a^2 + b^2), (a^2 - b^2), (2ab)]

MN = (1/2) × LN

LM = (√3/2) × LN

XY = XZ = (1/√2) × ZY

QS^2 = PS × SR

△ADB ~ △ABC

△BDC ~ △ABC

AB^2 = AD × AC

BC^2 = DC × AC

For triangle PQR with angle PQR = 90 degrees, PR is the hypotenuse.

In triangle LMN with angle L = 30 degrees, angle N = 60 degrees, and angle M = 90 degrees, MN = (1/2) x LN and LM = (sqrt(3)/2) x LN.

Use PR^2 = PQ^2 + QR^2 in triangle PQR with angle PQR = 90 degrees.

If the acute angles are 30° and 60°, then the side opposite 30° is half the hypotenuse and the side opposite 60° is (√3/2) times the hypotenuse.

If the acute angles are 45° and 45°, then each perpendicular side is (1/√2) times the hypotenuse.