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Flowchart Proof


Flowchart Proof

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 11 and 22 are complementary. If 1 and 3 are congruent, then2 and 3 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 1\angle 1 and 2\angle 2 are complementary means that their sum is 90.90^\circ.

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

The next step is to substitute m1=m3.m\angle 1=m\angle 3. This is called the Property of Equality.

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

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