2.2.1 Algebraic Proof (continued)

Example 3 Solving an Equation in Geometry

In this example, the figure and the solving steps are given, and the steps must be justified using postulates, definitions, properties, or information that is given. To determine the justification, consider the corresponding equation and the equation that precedes it. Determine how the equation has changed and then identify the property, postulate, or definition that allows such a change. For example, consider step 6, the final step. The corresponding equation is x = 5. The equation that precedes this is − 3 x = − 15. In order to get from − 3 x = − 15 to x = 5, the preceding equation must be divided by − 3. The property that allows this change is the Division Property of Equality.

Example 4 Identifying Properties of Equality and Congruence

Equality and congruence are similar, but equality is used to describe a relationship between numbers or things that represent numbers (such as variables) and congruence describes a relationship between figures. These three properties of congruence are similar to the Reflexive, Symmetric, and Transitive Properties of Equality.

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