Geometry Memorization Terms

Sin 45

√2/2

Cos 45

√2/2

Tan 45

1

Sin 30

1/2

Cos 30

√3/2

Tan 30

√3/3

Sin 60

√3/2

Cos 60

1/2

Tan 60

√3

Equation of a Circle with center at origin

x² + y² = r²

Equation of a Circle in Standard Form

(x-h)² +(y-k)² = r²

Formula for sum of interior angles

n - 2 ⋅ 180

Sum of exterior angles

360 degrees

Formula for each interior angles

(n-2) ⋅ 180/n

Formula for each exterior angles

360/n

Parallelograms properties

1. Opposite sides are parallel

2. Opposite sides are congruent

3. Opposite angles are congruent

4. Consecutive angles are supplementary

5. Diagonals bisect each other

6. Diagonals form 2 congruent triangles are congruent

Rhombus Properties

1. Parallelogram Properties

2. 4 congruent sides

3. Diagonals are perpendicular

4. Diagonals bisect opposite angles

Square Properties

1. Parallelogram Properties

2. A mix of a rhombus and a rectangle

Rectangle Properties

1. Parallelogram Properties

2. 4 right angles

3. Diagonals are congruent

Kites Properties

1. 2 pairs of adjacent, congruent sides

2. 1 pair of opposite angles are congruent

3. Diagonals are perpendicular

Trapezoid Properties

1 pair of parallel sides

Isosceles Trapezoid Properties

1. Properties of a Trapezoid

2. Legs are congruent

3. Base angles are congruent

4. Diagonals are congruent

Measure of angle formed when 2 secants intersect INSIDE a circle

m<1 = ½ (x + y)

Measure of angle formed when

1. 2 secants intersect OUTSIDE a circle

2. When a secant and tangent intersect

3. When two tangents intersect

m<1 = ½ (x - y)

Segment lengths when CHORDS intersect WITHIN a circle

a ⋅ b = c ⋅ d

Segment lengths when secants intersect OUTSIDE a circle

a ⋅ (a + b) = c ⋅ (c + d)

Segment lengths when a SECANT and TANGENT

a² = b(b + c)

p ^ q

p and q

Conjunction

p v q

p or q

Disjunction

Bi-conditional

p if and only if q; when both conditional and converse are true

Law of detachment

A possibility is provided where one thing is dependent on the other. One part of the possibility is then provided; hence, the second can be assumed.

Law of Syllogism

p → q

q → r

p → r

(Like the transitive property)

Line Symmetry

mapping a figure onto itself by folding it across the line of reflection.

Point Symmetry

Figure rotated about a point 180° and looks identical to original.

Rotational Symmetry

When a figure matches itself after undergoing some rotation with a partial turn.

Central Angles

m<1 = arc measure

The central angle is equal to the arc measure

Inscribed Angles

m<1 = ½ mAC

m<1 is half of the arc measure

Inscribed Quadrilaterals

Opposite angles are supplementary

Arc Length Formula

ℓ = x/360 ⋅ 2πr

Area of Sector Formula

x/360 ⋅ πr²

Scale Factor Ratio

a : b

Surface Area Ratio

(a/b)²

Volume Ratio

a³ : b³

90° clockwise rotation

(y, -x)

270° counterclockwise rotation

(y, -x)

90° counterclockwise rotation

(-y, x)

270° clockwise rotation

(-y, x)

180° rotation

(-x, -y)

line of reflection: y=x

The x and y values are switched

line of reflection: y = -x

The x and y values are switched. Then negate both values