**The Structure of a Proof**

- Draw the figure that illustrates what is to be proved.
- List the given statements, and then list the conclusion to be proved.
- Mark the figure according to what you can deduce about it from the information given.
- Write the steps down carefully, without skipping even the simplest one.

Contents

## What are the 3 Proofs in geometry?

Two-column, paragraph, and flowchart proofs are three of the most common geometric proofs. They each offer different ways of organizing reasons and statements so that each proof can be easily explained.

## How do you write a proof?

Write out the beginning very carefully. Write down the definitions very explicitly, write down the things you are allowed to assume, and write it all down in careful mathematical language. Write out the end very carefully. That is, write down the thing you’re trying to prove, in careful mathematical language.

## Are geometry proofs necessary?

Geometrical proofs offer students a clear introduction to logical arguments, which is central to all mathematics. They show the exact relationship between reason and equations. More so, since geometry deals with shapes and figures, it opens the student’s brains to visualizing what must be proven.

## Are proofs hard?

Proof is a notoriously difficult mathematical concept for students. Furthermore, most university students do not know what constitutes a proof [Recio and Godino, 2001] and cannot determine whether a purported proof is valid [Selden and Selden, 2003].

## How do you do proofs easily?

Practicing these strategies will help you write geometry proofs easily in no time:

- Make a game plan.
- Make up numbers for segments and angles.
- Look for congruent triangles (and keep CPCTC in mind).
- Try to find isosceles triangles.
- Look for parallel lines.
- Look for radii and draw more radii.
- Use all the givens.

## Who is the father of geometry?

Euclid, The Father of Geometry.

## What are the three ways of writing a proof?

There are many different ways to go about proving something, we’ll discuss 3 methods: direct proof, proof by contradiction, proof by induction.

## What’s SSS in geometry?

SSS ( side-side-side ) All three corresponding sides are congruent. SAS (side-angle-side) Two sides and the angle between them are congruent.

## How do you do congruency?

For two triangles to be congruent, one of 4 criteria need to be met.

- The three sides are equal (SSS: side, side, side)
- Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
- Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)