SYMKC Geometry

Pythagorean Theorem

a²+b²=c²

Trigonometry

sinθ=b/c
cosθ=a/c
tanθ=b/a

Parts of a Triangle

a: altitude or height
b: base (midpoint)
c: angle bisector

Ratio of Sides

a:b

Ratio of Perimeters

a:b

Ratio of Areas

a²:b²

Ratio of Volumes

a³:b³

Triangle Congruence

1. SSS
2. AAS
3. SAS
4. ASA
5. HL

Conditional Statement

P → Q

Converse Statement

Q → P

Inverse Statement

∼P → ∼Q

Contrapositive Statement

∼Q → ∼P

Square Perimeter

4s

Rectangle Perimeter

2l+2w

Circumference of a Circle

2πr

45-45-90 Rule

30-60-90 Rule

Square Area

s²

Rectangle Area

lw

Parallelogram Area

bh

Trapezoid Area

½ (b₁+b₂) h

Circle Area

πr²

Right Triangle Area

½ bh

Any Triangle (Heron's Formula)

√s(s-a)(s-b)(s-c)

Equilateral Triangle Area

Regular Polygon Area

½ ap

Cube Surface Area

6s²

Sphere Surface Area

4πr²

Cylinder Surface Area

2πr² + 2πrh

Complementary Angles

add up to 90°

Supplementary Angles

add up to 180°

Cube Volume

s³

Prism Volume

Bh

Cylinder Volume

πr²h

Pyramid Volume

1/3 Bh

Cone Volume

Sphere Volume

Volume Measurement

cubic units

Parts of a Circle

diameter
chord
semicircle
tangent
radius

Triangle Interior Angle Sum

180°

Quadrilateral Interior Angle Sum

360°

Regular Polygon Interior Angle Sum

180° (n-2)

Arc Length

s=θr

Sector Area

½ r²θ

√2

1.4

√3

1.7

3 Sides

triangle

4 Sides

quadrilateral

5 Sides

pentagon

6 sides

hexagon

7 Sides

heptagon (septagon)

8 Sides

octagon

9 Sides

nonagon

10 Sides

decagon

Polygon Parts

interior angle
diagonal
exterior angle
vertex
side