Scalar product : The scalar product of two vectors $\begin{pmatrix}a_1\\a_2\\ \vdots \\a_n\\\end{pmatrix}$ and $\begin{pmatrix}b_1\\b_2\\ \vdots \\b_n\\\end{pmatrix}$ is defined by $\begin{pmatrix}a_1\\a_2\\ \vdots \\a_n\\\end{pmatrix}\cdot\begin{pmatrix}b_1\\b_2\\ \vdots \\b_n\\\end{pmatrix}=a_1b_1+a_2b_2\ldots+a_nb_n.$ The scalar product is equal to the product of the norms of the two vectors times the cosine of the angle between the two vectors.

Divisible : An integer $x$ is called divisible by an integer $y$ if the division $x:y$ has a remainder of zero. For example 4 is divisible by 2 but 5 is not divisible by 2.

Factor : If a natural number is divisible by a second natural number, that second natural number is called a factor of the first natural number. For example the factors of 12 are 1,2,3,4,6 and 12.

Number : A number $x$ is a mathematical symbol representing a quantity.

Congruence : Two shapes are called congruent if they have the same shape and size. Two integers are called congruent modulo $x$ if they have the same remainder in a division by $x.$

Dilation : A transformation that changes the size of a shape while keeping the shape the same.

Reflection : A reflection is a transformation that mirrors a shape at a line. Reflections turn shapes into congruent shapes.

Rotation : A rotation is a transformation that turns a shape around. A rotation turns shapes into congruent shapes.

Shape : A shape is a set of points in space.

Similarity : Two shapes are called congruent if they have the same shape and size. Corresponding angles are the same in similar shapes and the ratio of corresponding side length is constant.

Square : A square is a quadrilateral with four right angles and four equal length sides. A square is a special case of a rectangle and a special case of a rhombus.

Translation : The transformation that moves a shape around without changing its size or shape.