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.

Corner : A corner of a shape is a point in the shape such that this point does not lie on the line segment between any two other points in the shape. Every triangle has 3 corners and every quadrilateral has 4 corners.

Perimeter : The perimeter of a two-dimensional shape is the length of the boundary of the shape. For a polygon this is the same as the sum of all the side lengths. For example a triangle with side lengths 1, 2 and 3cm has a perimeter of 1+2+3=6cm. The perimeter of a circle is referred to as its circumference.

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

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 $180^{\circ}.$

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.

Degree : For angles one degree is defined as the angle represented by a $\frac{1}{360}$ of the angle represented by a full circle. For measuring temperatures one can use either degrees Celsius or degrees Fahrenheit. In a polynomial the degree describes the highest exponent of $x$ that has a non-zero coefficient. For example the degree of $1+x+x^2$ is 2.

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

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.

Sum : A sum is the result of an addition.

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.

Prism : A prism is a polyhedron with two parallel base faces of the same shape and size and edges that connect corresponding corners of those two base faces. All the other faces besides the base faces are parallelograms.

Ray : A ray AB is a one-dimensional shape that includes the points A and B, all the points of the line segment AB and all the points of the straight extension of the line segment beyond B. The ray AB has exactly one endpoint namely A.

Rectangle : A rectangle is a quadrilateral with 4 right angles. Two opposing sides in a rectangle have the same length. They are sometimes referred to as the width and the length of the rectangle. To calculate the area of an rectangle one can multiply the width of the rectangle by the length of the rectangle. A square is the special case of a rectangle in which all side lengths are the same. Every rectangle is a parallelogram.

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

Three-dimensional shape : A three-dimensional shape is a shape that has a volume.

Volume : Volume refers to the size of a three-dimensional objects measured by how many unit cubes it would take to fill the shape.