Addition : Addition is the mathematical operation that describes increasing a number by an amount equal to a second number. The mathematical symbol for addition is the plus sign $+.$ The term addition is also used for a generalization of this basic operation on numbers to functions, vectors and matrices.

Adjacent corner : Adjacent corners in a polygon are corners that are linked by a side.

Adjacent side : Adjacent sides in a polygon are sides that share a corner.

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.

Diagonal : A diagonal in a quadrilateral is the line segment between a corner and its opposing corner. A diagonal in a cube (or rectangular prism) is the line segment between two corners that are not part of a same face.

Kite : Kites are quadrilaterals with two pairs of adjacent sides of equal length.

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

Quadrilateral : A quadrilateral or quadrangle is a polygon with four corners. Rectangles, trapezoids, kites, rhombuses, squares and parallelograms are all specific kinds of quadrilaterals. The sum of the interior angles in a quadrilateral is always $360^{\circ}.$

Right angle : A right angle is an angle equal to $90^{\circ}.$

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.

Straight angle : A straight angle is an angle equal to $180^{\circ}.$

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 $180^{\circ}.$

Boundary : The boundary of a 2-dimensional shape is the 1-dimensional shape that separates the 2-dimensional shape from the rest of the 2-dimensional space.

Circle : A circle is a two-dimensional shape. The boundary of a circle is a set of points that has the same distance (the radius) from the center of the circle.

Constant : Constant is another word for a fixed number that is mainly used in the context of expressions or functions like $f(x)=c$ that are equal to the same number irrespective of any variable.

Ellipse : An ellipse is a two-dimensional shape with a boundary that is a set of points for which the combined distance from two points is constant. Circles are special cases of ellipses. The boundary of an ellipse can also written as the set of points $\{(x,y)| \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \}$

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

Set : A set is a collection of objects.

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.

Line segment : A line segment AB is a one-dimensional shape consisting of the points A and B and all the points on the straight connection of A and B. A and B are both endpoints of the line segment AB.

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.

Ratio : A ratio is a comparison of two numbers using a division.

Similar triangle : A similar triangle is a triangle with the same shape but not necessarily the same size. Ratios of corresponding side lengths and corresponding angles are the same in similar triangle. This fact is used to be able to uniquely define the trigonometric functions using ratios of side lengths in right triangles. Two triangles are similar if they share two angles (and therefore all three) or if all 3 ratios of the lengths of corresponding sides in the two triangles are the same. Two triangles are also similar if two ratios of lengths of corresponding sides in the two triangles are the same and the angle between the two sides in the two triangles is the same.