A flowchart proof is a compact way showing the logic and reasoning behind a mathematical proof. It's a flowchart with statements in boxes and the reasoning on the right-hand side. The reasoning can be postulates, theorems, or other mathematical reasoning that the reader is assumed to be able to follow without difficulty.

To show how to build a flowchart proof, consider the following figure.

Angles $1$ and $2$ are complementary. $\begin{aligned} &\text{If $\angle 1$ and $\angle 3$ are congruent, then} \\ &\text{$\angle 2$ and $\angle 3$ are complementary.} \end{aligned}$ First, write the given information in the first box.

The fact that $\angle 1$ and $\angle 2$ are complementary means that their sum is $90^\circ.$

Since $\angle 1$ and $\angle 3$ are congruent they have the same measure.

The next step is to substitute $m\angle 1=m\angle 3.$ This is called the Property of Equality.

Since the sum of $\angle 3$ and $\angle 2$ is $90^\circ,$ they are complementary.

Therefore, $\angle 2$ and $\angle 3$ are complementary. The proof is complete.