ACT: Geometry and Trigonometry

Coordinate Geometry

Distance Formula

$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

Midpoint

$M = \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$

Plane Geometry

Triangles

• Angle sum: $180$
• Area: $A = \frac{1}{2}bh$
• Pythagorean theorem: $a^2 + b^2 = c^2$

Circles

• Area: $A = \pi r^2$
• Circumference: $C = 2\pi r$

Polygons

• Interior angles sum: $(n-2) \cdot 180$

Trigonometry

SOH CAH TOA

$\sin \theta = \frac{\text{opp}}{\text{hyp}}$ $\cos \theta = \frac{\text{adj}}{\text{hyp}}$ $\tan \theta = \frac{\text{opp}}{\text{adj}}$

Law of Sines

$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$

Law of Cosines

$c^2 = a^2 + b^2 - 2ab\cos C$

Special Right Triangles

• 30-60-90: $x : x\sqrt{3} : 2x$
• 45-45-90: $x : x : x\sqrt{2}$

ACT Tip: Geometry formulas are NOT provided. Memorize them.