Method

Flowchart Proof

A flowchart proof is a graphical way of showing the logic of a mathematical proof, with statements in boxes and supporting reasons below. These reasons may include postulates, theorems, or other mathematical reasoning assumed to be understandable. For example, consider the following diagram.

The claim can be proved using a flowchart. Follow the next three steps.

Write the Given Information in Boxes

Begin the proof by writing the given information inside a box. In this case, since two statements were given, they should be labeled accordingly.

Develop Logical Conclusions

Begin with the given information and create logical statements to prove the desired result. Make sure to connect these statements with arrows. For example, the fact that

∠ 1

and

∠ 2

are complementary means that their measures add up to

9 0^{\circ} .

m ∠ 1 + m ∠ 2 = 9 0^{\circ}

Write this equation below the first box.This equation can be included because of the definition of complementary angles. Note this reason below the corresponding box.

Repeat Step

2

as Needed

The statements written so far are not enough to reach to the desired conclusion. Keep deriving information and combining it until it points to the desired statement. By definition, Congruent angles have the same measure.

∠ 1 ≅ ∠ 3 ⇓ m ∠ 1 = m ∠ 3

Write this equation below the corresponding box along with its reason.

Next, substitute $m ∠ 3$ for $m ∠ 1$ into the equation for the sum of the measures. This is justified by the Substitution Property of Equality.

The measures of $∠ 2$ and $∠ 3$ add up to $9 0^{\circ} .$ Therefore, these angles are complementary.

Notice that the last statement is the desired one. Therefore, the proof is complete!

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