# Writing Formal Proofs in Geometry

## What is a formal proof?

A large number of the questions in geometry contain proofs. Therefore, one must study the correct and formal way to write them. When we are asked to prove a certain claim, in fact, we have to construct a series of arguments that, each of them, must be accompanied by some explanation or justification. The explanation or justification can be some data, calculation, or some theorem. Finally, the last argument of the proof is based on the previous ones and confirms what we wanted to prove.

We will illustrate this with a simple example.

Given the triangle $\triangle ABC$. We must prove that the triangle $\triangle ABC$ is an isosceles triangle.

### The Formal Proof

 Angle A measures 40 degrees Given Angle B measures 70 degrees Given El ángulo C mide 70 grados According to the theorem: the sum of the angles of a triangle is equal to 180 degrees, we will calculate 180-70-40= 70. From the above, we can demonstrate that triangle ABC is an isosceles triangle. According to the theorem: the isosceles triangle is a triangle in which the base angles are equal

QED

The angles $B$ and $C$ are the base angles and measure $70º$

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Congruence Criterion: Side, Angle, Side

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Congruence Criterion: Side, Side, Side

Side, side and the angle opposite to the larger of the two sides

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