Geometry — Cheat Sheet

ANGLE PAIRS

Complementary

sum = 90°

Supplementary

sum = 180°

Vertical

opposite — equal

On a line

sum = 180°

At a point

sum = 360°

PARALLEL LINES + TRANSVERSAL

Corresponding

F-shape — EQUAL

Alternate int.

Z-shape — EQUAL

Co-interior

C-shape — sum 180°

F = equal, Z = equal, C = 180°

TRIANGLE ANGLES

Interior sum

A + B + C = 180°

Exterior angle

= sum of 2 non-adjacent interior

Quadrilateral

sum = 360°

PERIMETER FORMULAS

Square

P = 4s

Rectangle

P = 2(l + w)

Triangle

P = a + b + c

Circle (C)

C = 2πr = πd

AREA FORMULAS

Square

A = s²

Rectangle

A = l × w

Triangle ★

A = (b × h) / 2

Parallelogram

A = b × h

Trapezoid

A = ((b₁+b₂)/2) × h

Circle

A = πr²

⚠ Height must be perpendicular to base!

VOLUME FORMULAS

Rect. prism

V = l × w × h

Cylinder

V = πr²h

Triangular prism

V = base area × h

Pyramid/cone

V = (1/3) × base × h

Sphere

V = (4/3)πr³

SURFACE AREA

Rect. prism

SA = 2(lw + lh + wh)

Cylinder

SA = 2πr² + 2πrh

Sphere

SA = 4πr²

Draw a net to identify all faces
Area in cm² · Volume in cm³

PYTHAGOREAN THEOREM

Formula ★

a² + b² = c²

Hypotenuse

c = √(a² + b²)

Leg

a = √(c² − b²)

Only for right triangles!
c is always opposite the right angle

Legs 6, 8: c = √(36+64) = √100 = 10
Hyp 13, leg 5: b = √(169−25) = √144 = 12

PYTHAGOREAN TRIPLES

3-4-5

and multiples: 6-8-10 …

5-12-13

and multiples: 10-24-26

8-15-17

—

COMMON MISTAKES

Triangle angles = 180° (not 360°)
Height ⊥ base in area formulas
Pythagoras: right triangles ONLY
c is the hypotenuse (longest side)
C = 2πr, A = πr² (don't mix them)