geo formulas

Supplementary Angles

a + b = 180 degrees.

Complementary Angles

a + b = 90 degrees.

Vertical Angles

Angles that are equal (congruent).

Parallel Lines Cut by a Transversal - Alternate interior angles

Are congruent.

Parallel Lines Cut by a Transversal - Corresponding angles

Are congruent.

Parallel Lines Cut by a Transversal - Same-side interior angles

Are supplementary.

Area of a Triangle

A = 1/2 * base * height.

Pythagorean Theorem

a^2 + b^2 = c^2 for right triangles.

Triangle Sum Theorem

a + b + c = 180 degrees.

45°-45°-90° Triangle Ratio

x : x : x√2.

30°-60°-90° Triangle Ratio

x : x√3 : 2x.

Circumference of a Circle

C = 2πr or πd.

Area of a Circle

A = πr².

Arc Length Formula

(θ / 360) * 2πr.

Sector Area Formula

(θ / 360) * πr².

Equation of a Circle

(x - h)² + (y - k)² = r².

Area of a Rectangle/Square

A = base * height.

Area of a Trapezoid

A = 1/2 (b1 + b2) * h.

Area of a Parallelogram

A = b * h.

Volume of a Prism/Cylinder

V = B * h.

Surface Area of Cylinder

SA = 2πr² + 2πrh.

Volume of a Pyramid/Cone

V = 1/3 * B * h.

Surface Area of Cone

SA = πr² + πrl.

Volume of a Sphere

V = 4/3 πr³.

Surface Area of Sphere

SA = 4πr².

Distance Formula

√((x2 - x1)² + (y2 - y1)²).

Midpoint Formula

((x1 + x2)/2, (y1 + y2)/2).

Slope Formula

(y2 - y1)/(x2 - x1).