Math: Geometry

Question 1

Traingle

Answer 1

Features:

1. Three Sides
2. Angles add up to 180^o

Area:

Area = (1/2) * Base * Height

Perimeter:

Perimeter = Sum of All Sides

Question 2

Special Right Triangles (Sides)

Answer 2

3: 4:5
5: 12:13
8: 15:17

Question 3

30-60-90 Triangle

Answer 3

A triangle with the angles 30, 60, and 90 always has sides with lengths of the proportions 1x, √3x, 2x.

1x is the shortest side.

√3x is the second longest side.

2x is the hypotenus.

Question 4

45-45-90 Triangle

Answer 4

A triangle with the angles 45-45-90, always has sides with lengths of the proportions 1x, 1x, √2x.

The two short sides are in proportion x.

The hypotenuse is in proportion √2x.

Question 5

Isosceles Triangle

Answer 5

An isosceles triangle has at least two sides and two angles that are the same.

Question 6

Equilateral Triangle

Answer 6

In an equilateral triangle, all sides are of equal length and all angles are 60^o.

The height of an equilateral triangle is (√3)/2 times the side of an equilateral triangle.

Question 7

Square

Answer 7

Features:

• Every side is the same length and opposite sides are parallel.
• Every angle is 90^o.

Area:

Area = L² = Length * Width

Perimeter = 4L

Question 8

Rectangle

Answer 8

Features:

• Opposite sides are parallel and of the same length.
• Every angle is 90^o.

Area:

Area = Length * WIdth

Perimeter:

Perimeter = 2L * 2W

Question 9

Parallelogram

Answer 9

Features:

• Opposite Sides are Parallel and of the same length.
• The interior angles add up to 360^o.

Area:

Area = Base * Height

Perimeter = 2a * 2b

Question 10

Trapezoid

Answer 10

Features:

• Two side are parallel.
• The interior angles add up to 360^o.

Area:

Area = 1/2*(b₁+b₂)*Height

Perimeter = Sum of Four Sides

Question 11

Key Circle Definitions

Answer 11

Radius: The radius of a circle describes the distance from the center of a circle to the circle itself.

Diameter: The diameter of a circle describes the distance from one side of the circle to the other side, intersecting the center of the circle. D = 2R

Chord: A line that connects any two points on a circle.

**Area: **

Area = π * (r²)

Circumference:

Circumference = 2πr = dπ

Central Angle: Any angle whose vertex is at the center of the circle.

Inscribed Angle: Any angle whose vertex is on the circumference of the circle.

Tangent: A line that touches a circle at only one point. The tangent is perpendicular to the radius at the point of tangency.

Question 12

Inscribed/Central Angle Rules

Answer 12

All inscribed angles that share the same arc or arcs of equal length are equal in measure.

Any inscribed angle tat shares the same arc as a central angle is exactly one-half the measure of the central angle.

Question 13

Line Formula (Coordinate Geometry)

Answer 13

Line Formula:

y = mx + b

m is slope; b is y-intercept

Question 14

Slopes of Perpindicular Lines

Answer 14

Lines that are perpendicular to one another will have slopes that are the negative reciprocals of each other.

Question 15

Slope Forumla (Coordinate Geometry)

Answer 15

Slope Formula:

Slope = (Change in Y) / ( Change in X)

Slope = (y₂ - y₁) / (x₂ - x₁)

X intercept is point at which y = 0.

Y intercept is point at which x = 0.

Question 16

Distance Formula (Coordinate Geometry)

Answer 16

Distance Formula:

Distance = √(x₁-x₂)²+(y₁-y₂)²

Question 17

Midpoint Formula (Coordinate Geometry)

Answer 17

Midpoint Formula:

Midpoint = [(x₁+x₂)/2, (y₁+y₂)/2]

Question 18

Arc Length Formula

Answer 18

Arc Length Formula:

Arc Length = Circumference * (Central Angle/360)

Question 19

Similar Triangles

Answer 19

Features:

• All angles are the same.
• Like sides are proportional (a/A = b/B = c/C = h/H)

Steps for Similarity

1. Determine Shapes Are Similar (SAS, SSS, AAA).
2. Calculate Ratio (Ø).

• For Lines, Ratio is Ø.
• For Area, Ratio is ز.
• For Volumes, Ratio is س

3. Multiply or Divide as Needed.