2.5 Algebraic Proof

Solving an equation in geometry

Write a justification for each step.

An algebraic proof uses ____ ____ such as the properties of equality and the Distributive Property.

Algebraic properties

Proof

An argument that uses logic, definitions, properties, and previously proven statements to show that a conclusion is true.

What is an important part of writing a proof?

Giving justifications to show that every step is valid. For each justification you can use a definition, postulate, property, or a piece of information that is given.

Just read

Like algebra, geometry also uses numbers, variables, and operations. For example, segment lengths and angle measures are numbers. So you can use the same properties of equality write algebraic proofs in geometry.

As you have learned, if you start with a true statement and each logical step is valid, then your conclusion is ____.

Valid

Just read.

You have learned that segments with equal lengths are congruent and angles with equal measures are congruent. So the Reflexive, Symmetric, and Transitive Properties of Equality have corresponding properties of congruence.