# Flow Proof in Geometry: Definition & Examples

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Lesson Transcript
Instructor: Mia Primas

Mia has taught math and science and has a Master's Degree in Secondary Teaching.

When someone claims something is true, it's important that they are able to support the claim with proof. In this lesson, you will learn how flow proofs are used in geometry to support a mathematical claim.

## Background on Mathematical Proofs

Throughout the history of mathematics, a proof has been a series of statements that lead to a conclusion. Proofs begin with one or more given statements, which are provided. The given statement leads to other statements until the desired conclusion is reached. Each statement in a sequence must be supported with logical reasoning. Mathematical properties, definitions, and theorems are used to validate the statements.

When working with geometry proofs, it is important to be familiar with properties, definitions, and theorems that can be used to validate each statement. For example, if you're asked to prove that two triangles are congruent, it's useful to know the theorems of congruent triangles. Or, if a proof involves a rectangle, you may need to use the properties of the sides and angles of rectangles to support your reasoning.

Proofs can be presented in different formats, such as a paragraph, a two-column chart, or a flow chart. In a paragraph proof, the statements and reasons are written as sentences. In a two-column proof, the statements are written in one column, and the reasons are written next to them in a second column. A flow proof uses a diagram to show each statement leading to the conclusion. Arrows are drawn to represent the sequence of the proof. The layout of the diagram is not important, but the arrows should clearly show how one statement leads to the next. The explanation for each statement is written below the statement.

The following examples will detail each proof in paragraph form, followed by a flow chart. The examples begin with the given information, along with the desired conclusion to be proven.

## Proving Congruency

Our first example begins with the figure of quadrilateral ABCD and the given statement telling us that it's a rectangle. One of the properties of rectangles is that the opposite sides are congruent to each other. We can use this to show that side AD is congruent to side BC and side AB is congruent to side CD. The reflexive property tells us that any line segment is congruent to itself; therefore, side AC is congruent to side AC. We now have three pairs of congruent sides. Using the Side-Side-Side theorem of triangle congruency, we've proven that triangle ACD is congruent to triangle CAB.

## Proving that a Triangle Is Isosceles

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