Alternate interior angle : When two parallel lines are crossed by a third line, alternate interior angles are a pair of angles that are between the two parallel lines and are on opposites sides of the crossing line. Alternate interior angles are equal.

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.

Follow from : A second equation or inequality follows from an initial equation or inequality if all solutions of the initial equation are also solutions from the second equation or inequality. It does not necessarily have to be the case that all solutions of the second equation or inequality have to by solutions of the first inequality. For example $x^2=1$ follows from $x=1$, but $x^2=1$ is not equivalent to $x=1$ as -1 is a solution of $x^2=1$ but not a solution of $x=1.$

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.

Proof : A proof is a logical deduction of a result starting only with the assumptions of the result.

Pythagorean theorem : The Pythagorean theorem states that in a right triangle the square of the hypotenuse $c^2$ equals the sum of the squares of the legs $a^2+b^2$. It can be used to calculate the length of a third side of a right triangle given the other two. It also can be used to calculate the lengths of diagonals in rectangles or cubes.

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

Sum : A sum is the result of an addition.

Thales' theorem : Given a circle, points A, B and C on the circle such that the line segment AB goes through the center of the circle, the theorem of Thales says that the angle ACB is a right angle making ABC a right triangle. Thales' theorem is a special case of the inscribed circle theorem.

Theorem : A mathematical result that has been proven to hold true under the assumptions that are stated in the theorem. The most famous theorems have name like for example the Pythagorean theorem or Fermat's little theorem.

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 $180^{\circ}.$