Angle : If two line segments (or rays) both start at a common point the opening between the two line segments is called an angle. The common point is called vertex of the angle. The size of an angle is measured in degrees.

Counterexample : A counterexample to a statement of the form 'all objects of type x have property y' is an object of type x that does not have property y. A counterexample to a statement shows that the statement is not true in general. For example the number 3 is a counterexample to the statement that all numbers are even.

Equilateral : A polygon that has side lengths that are all equal is called equilateral polygon.

Length : Length is the attribute of a one-dimensional shape that can be measured with a measuring tape.

Line : A line AB is a one-dimensional shape that includes the points A and B, all the points on the line segment in between A and B and all the points of the straight extension of the line segment beyond A and B. A line does not have an endpoint.

Parallel : Two lines in a two-dimensional plane are called parallel if they never cross.

Point : A point is an element in a space. Shapes are made of sets of points.

Polygon : A polygon is a two-dimensional shape which has a boundary with $N\geq 3$ corners $C_1, C_2,\ldots C_N$ and edges equal to the line segments $C_1C_2$, $C_2C_3$,..., $C_{N-1}C_{N}$ and $C_NC_1.$ Triangles, quadrilaterals and octagons are all examples of polygons.

Basis : The basis of a vector space is a set of linearly independent vectors, so that every vector of the vector space can be written as a linear combination of the vectors in the basis. For example $\{\left(\begin{smallmatrix}1\\0\\0\\\end{smallmatrix}\right),\left(\begin{smallmatrix}0\\1\\0\\\end{smallmatrix}\right),\left(\begin{smallmatrix}0\\0\\1\\\end{smallmatrix}\right)\}$ is a basis of $\mathbb{R}^3.$ In a prove by induction basis refers to the first step in which you have to prove that the result is true for a particular number $n$ (usually $n=0$ or $n=1$.)

Independence : Random variables $X,$ $Y$ are called independent if $P[X\in A, Y\in B]=P[X \in A]P[Y \in B].$ Independent identically distributed random variables feature prominently in the law of large numbers and the central limit theorem. Vectors $x_1,x_2\ldots, x_n$ are called linearly independent if $\lambda_1 x_1+\lambda_2 x_2+\ldots+\lambda_n x_n=0$ implies $\lambda_1=\lambda_2=\ldots=\lambda_n=0.$

Linear independence : Vectors $x_1, x_2,\ldots, x_n$ in a vector space are called linearly independent if $\lambda_1 x_1+\lambda_2x_2+\ldots+\lambda_nx_n=0$ implies $\lambda_1=\lambda_2=\ldots=\lambda_n=0.$ In other words vectors are linearly independent if the only linear combination of the zero vector is the trivial one in which all coefficients are zero.

Three-dimensional coordinate vector space : The vector space of all three-dimensional vectors $\begin{pmatrix}a\\b\\c\\\end{pmatrix}.$

Vector : Most commonly vector refers to a matrix with one column $\begin{pmatrix}x_1\\ \vdots \\x_n\\\end{pmatrix}.$ In general a vector is an element of a vector space.

Area : The amount of unit squares that is needed to cover a 2-dimensional shape.

Base : When using the height of a triangle or parallelogram (for example in an area calculation), base refers to the side of the triangle or parallelogram that the height starts out at. In a logarithm $\log_{b}x$ or power $b^x$ base refers to the number $b.$

Centimeter : A centimeter ($cm$) is $\frac{1}{100}$ of a meter.

Half : A Half is the number equal to $\frac{1}{2}=0.5.$

Height : In a triangle a height (or altitude) is the shortest line segment that connects a side to its opposing corner. A height of a triangle is perpendicular to the side is started at. The three heights of a triangle intersect in a point, the so called orthocenter of the triangle. In a parallelogram the height is the shortest distance between two opposing sides. In a pyramid the height is the shortest distance between the base area and the corner of the pyramid that is not part of the base area. In a prism the height is the shortest distance between the two base faces.

Product : A product is the result of a multiplication.

Square centimeter : Square centimeter or $cm^2$ is a unit of measurement for measuring area. 1 square centimeter is the area of a square with side length 1 $cm,$ so 10,000 $cm^2$ are one $m^2.$

Triangle : A triangle is a polygon with three corners and three sides. You can calculate the area of a triangle by multiplying half the length of the base by the height on that base. The sum of the interior angles in a triangle is always $180^{\circ}.$