Using notation for sizes

FullProof lets you denote the sizes of angles, lengths and areas with a Greek or Latin letter, and use that notation to write equations. Notation makes proofs much more efficient, which is why students and teachers like writing proofs this way.

Defining new notation

Each notation is defined only once; after defining it, you must explain each use of it to describe other sizes. You can define new notation in three ways:

In the diagram

When you click an angle or a segment in the diagram, a menu opens; under Value you can pick a letter or write an algebraic expression as its notation. For angles the menu offers the Greek letters alpha, beta and gamma, and for segments the letters a, b, c. In the field below them you can write any expression, with a keyboard that includes, among others, the degree sign, division (fraction), square root and powers.

In a statement

To denote the size of an angle or a segment, choose the statement type Denote Angle or Denote Segment, choose the element and write the notation. To denote the area of a polygon, choose Denote Area of Triangle or Denote Area of Quadrilateral, choose the polygon and write the notation S.

The reason Denote fills in automatically.

In an equation

Write the element/area you want to denote and the notation in the equation, and choose the reason Denote from the list of reasons.

You can define several equal elements together. Example: AB=AC=x

You can use any Latin letter, and the Greek letters in the equation editor, as notation. Example: AB=m

You can define it with an algebraic expression. Example: AB=2x

You can combine all of these: AB=AC=2k.

Using existing notation

When you use existing notation, write a suitable reason that explains why it is correct to use the notation the way you chose.

In the diagram

You can use the notation to set the size of an angle or a segment through its menu in the diagram. You can use the notation itself or an algebraic expression that includes it.

In a statement

You can use the notation in statements where another size equals the defined notation or is greater than it, or in statements where an angle's notation equals a number, or a notation equals another notation. Anything more complex must be written as an equation.

In an equation

We recommend writing equations with the explicit names of the angles before substituting notation and numbers. You don't need to write every intermediate step of a calculation in the system; it is enough to write the equation and its solution.