Studied by 19 people
Triangle Area
The area of a triangle is calculated using the formula A = 1/2 * base * height, where the base is any side of the triangle and the height is the perpendicular distance from the base to the opposite vertex.
Isosceles Right Triangle Angles
45,45,90
Isosceles Right Triangle Side Proportions
(45-45-90) has sides in a ratio of x:x:x√2
A 30-60-90 triangle has sides in a ratio of
A 30-60-90 triangle has sides in a ratio of x:x√3:2x, with the 1x side opposite the 30 degree angle.
Pythagorean Theorem
For a right triangle with legs a and b and hypotenuse c: 𝑐2=𝑎2+𝑏2c2=a2+b2. This is called the Pythagorean Theorem
Right Triangle longest side
A right triangle has a right angle (a 90 degree angle); the side opposite the right angle is called the hypotenuse, and is always the longest side.
Pythagorean triples
Each side of certain right triangles are integers. These sets of numbers are called Pythagorean triples: 3-4-5, 5-12-13, 8-15-17, 7-24-25. A multiple of a Pythagorean triple is a Pythagorean triple (e.g., 6-8-10)
Triangle Longest side compared to other two sides
The length of the longest side can never be greater than the sum of the two other sides
Triangle shortest side compared to other two sides
The length of the shortest side can never be less than the positive difference of the other two sides
Circle Area
Area=πr2
Circumference
Circumference=2πr
Arc
A circle has 360 degrees. An arc is the portion of the circumference of a circle in x degrees of the circle
A fraction of the circumference of a circle is called an arc. To find the degree measure of an arc, look at the central angle
Arc Length
Arc Length=𝑥/360*2πr
Area of sector
Area of sector=𝑥/360*π𝑟2
Chord
A chord is a line segment between two points on a circle. A chord that passes through the middle of the circle is a diameter
Inscribed angles with the same chord/arc
If two inscribed angles hold the same chord, the two inscribed angles are equal
Inscribed angles holding chords/arcs of equal length are equal.
Degrees of an inscribed angle holding the diameter
An inscribed angle holding the diameter is a right angle (90 degrees)
Polygon total degrees formula
180(n − 2)
Cube formulas
Cube volume=𝑠3
Cube surface area=6𝑠2
