point (geometry)

Represented by a dot and usually named by a capital letter. Used to mark geometric figures.

P

⋅

Line (geometry)

A line is an infinite set of points and is named by a small letter or two points on the line. For example a line defined by two points: A and B would be written as  [image]

[image]

Plane (geometry)

A flat surface. a two-dimensional doubly ruled surface spanned by two linearly independent vectors. Defined by 3 points.

A plane defined by the points A, B, and C, would be Plane ABC.

[image]

Line Segment (geometry)

A part of a line between two points (called endpoints).

[image]

Center, Diameter, Radius, and Circumference of a circle

Center is the dot in the middle of the circle

Radius is a line segment from the center of the circle.

Diameter is a line segment passing through the center of the circle. The diameter is made up of two radii (plural of radius)

Circumference is the perimeter of a circle

[image][image]

Perimeter

The distance around the outside of a geometric figure is called the perimeter and is found by adding the measures of all sides of the figure.

Formula: Perimeter of a triangle

P = a + b + c

Formula: perimeter of a rectangle

P = 2l+2w

(l stands for length; w stands for width)

Formula: perimeter of a square

P = 4s

Formula: circumference (perimeter) of a circle

C = πd

or

C = 2πr

Where d stands for diameter and r stands for radius. The diameter is calculated as 2r and the radius as ^d/₂ or d(¹/₂)

Π

mathematical constant

3.1415926535897932384626433

[image]

Area

The area of a geometric figure is the number of square units contained in its surface.

Formula: Area of a Rectangle

A = lw

(l is length; w is width)

Formula: area of a square

A = s²

(s is the length of the square sides)

Altitude of a Triangle

Altitude of a triangle is the measure of a perpendicular line from its apex to its base.

[image]

Formula: area of a triangle

A = ¹/₂bh

Formula: Area of a parallelogram

A = bh

Formula: Area of a Trapezoid

A = ¹/₂h(b₁+b₂₎

A trapezoid has two bases; base 1 (b₁), the lower base at the bottom of the trapezoid and base 2 (b₂), the upper base at the top of the trapezoid.

Formula: area of a circle

A = πr²

Volume

The volume of a geometric figure is a measure of its capacity. Volume is measured in cubic units. Cubic units are abbreviated using 3 for the exponent.

Volume of a rectangular solid

V = lwh

Volume of a cube

V =s³

Volume of a cylinder

V = πr²h

Volume of a sphere

V = ⁴/₃πr³

Volume of a right circular cone

V = ¹/3πr²h

Volume of a pyramid

The volume of a pyramid can be found by using the formula V = ¹/₃ Bh, where B is the area of the base and h is the height of the pyramid. If the base is a square, use B = s². If the base is a rectangle, use B = lw.

Pythagorean Theorem

For any right triangle c² = a² + b²

where c is the length of the hypotenuse and a and b are the lengths of its sides

[image]

hypotenuse of a right triangle

[image]

Find the value of opposite side of a right triangle with a hypotenuse of 13 and an adjacent side of 12.

b = √c² - a²

Where a is the adjacent side, and b is the opposite side

t = √13² - 12²

[image]

[image]

Ray

Ray is defined by two points but unlike a line it terminates at the first point (it's starting point) then goes on to infinity in only one direction.When writing a ray, list the starting point first follow by any point on it's endless journey. 

[image]

Anatomy of an angle

• Vertex: A vertex is a corner of an angle, a point where two lines/sides meet. O is the vertex in the given figure.
• Arms: The two sides of the angle, joined at a common endpoint. OA and OB are arms of an angle.
• Initial Side: Also known as the reference line, a straight line from where an angle is drawn. OB is the reference line.
• Terminal Side: The side up to which the angle measurement is done. In the given diagram below, OA is the terminal side.

[image]

Five types of Angles

• Acute Angles
• Obtuse Angles
• Right Angles
• Straight Angles
• Reflex Angles
• Full Rotation

Acute Angle

[image]

An acute angle lies between 0 degree and 90 degrees, or in other words; an acute angle is one that is less than 90 degrees. The figure above illustrates an acute angle.

Obtuse Angle

[image]

An obtuse angle is the opposite of an acute angle. It is the angle which lies between 90 degrees and 180 degrees or in other words; an obtuse angle is greater than 90 degrees and less than 180 degrees. The figure above illustrates an obtuse angle.

Right Angle

[image]

A right angle is always equal to 90 degrees. Any angle less than 90 degrees is an acute angle whereas any angle greater than 90 degrees is an obtuse angle. The figure above illustrates a right angle or a 90-degree angle.

Straight Angle

[image]

A straight angle is 180 degrees when measured. The figure above illustrates a straight angle or a 180-degree angle. You can see that it is just a straight line because the angle between its arms is 180 degrees.

Reflex Angle

[image]

Any angle that has a measure which is greater than 180 degrees but less than 360 degrees (which coincides with 0 degrees) is a reflex angle.

Positive Angle

[image]

An angle formed by an anti-clock wise or counterclockwise rotation from its initial side is called a positive angle. Thus 12°, 33°, 90°, 180°, 360° are all example of positive angles.

Negative Angle

[image]

An angle formed by a clockwise rotation from its initial side is called a negative angle. Thus -9°, -45°, -110°, -280°, -310° are all example of negative angles.

supplementary angles

the sum of two angles is equal to 180°