Flow charts are one of the many ways to write a geometric proof. Column and paragraph proofs contain all of the same information as flow charts, but flow chart proofs graphically represent the logical flow of the proof. In a flow chart proof, you connect statements and conclusions with arrows. In order to connect the given information to its logical conclusions, you must be familiar with many axioms and theorems of triangles and geometry in general.

## Step 1

Write all of the given pieces of information in individual boxes. For example, suppose you are given a diagram with two parallel line segments AC and DE. Suppose you are also given two line segments AE and CD, intersecting at point B. Lastly, suppose you are told that angle BDE equals angle BED. You can then write "line segment AC is parallel to line segment DE" and "angle BDE equals angle BED" in two separate boxes.

## Step 2

Write what you are asked to prove in an individual box far below or to the right of your given information. For example, if you are asked to prove that triangle ABC is isosceles, write "triangle ABC is isosceles" in a box far from your given information.

## Step 3

Draw an arrow from a box containing given information to a new box containing the information that follows from that statement. For example, draw an arrow from the box containing "line segment AC is parallel to line segment DE" to a new box containing "angle ACB equals angle BDE." You can also write an arrow from the box containing "line segment AC is parallel to line segment DE" to a new box containing "angle CAB equals angle BED."

## Step 4

Write the theorems or principles that establish a piece of information underneath that statement. For example, underneath both of the new boxes, you can write "alternate interior angles are equal."

## Step 5

Draw arrows from the various pieces of information to a new box containing a conclusion that follows from their combination. For example, draw arrows from the boxes containing "angle BED equals angle BDE," "angle CAB equals angle BED" and "angle ACB equals angle angle BDE" to a new box containing the statement "angle ACB equals angle CAB."

## Step 6

Write the reason for this new conclusion underneath the box. For example, underneath "angle ACB equals angle CAB," write "transitive property."

## Step 7

Draw arrows to new boxes containing any further conclusions. Under these boxes, write the reason for this new conclusion. For example, connect "angle ACB equals angle CAB" to "AB equals CB." Write "converse of isosceles triangle theorem" underneath this box.

## Step 8

Survey the information in each box. If you have enough information to conclude your proof, draw arrows from the boxes containing that information to the statement you need to prove. For example, draw an arrow from the box containing "AB equals CB" to the box containing "triangle ABC is isosceles."

## Step 9

Write the reason for the last logical connection underneath the box containing the statement you wish to prove. For example, underneath "triangle ABC is isosceles," write "definition of isosceles triangle."

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