Geometry

Section 2.5 Reasoning in Algebra and Geometry

2.5: Reasoning in Algebra and Geometry:

Goal: You will know how to solve problems in algebra and geometry and use properties to justify each step you take.

You will use deductive reasoning to construct proofs. These proofs will use POSTULATES, PROPERTIES, or DEFINITIONS to justify each step.

In the examples below, refer to the definitions and postulates we have learned, and the sheet of properties justify statements.

Example 1: Justifying Steps of an equation.

Solve for x:

Statements

Reasons

Example 2: Identify which property is being used .

a. 2x + 9 = 19 b. c.

2x = 10

Example 3: Two-Column Proof

a. Given:

Prove:

Statement

Reasons

b. Given:

Prove:

Below are list of the key properties you will use in proofs:

Here are algebraic properties of equality:

Here are the key properties of congruence

Here is the distributive property

Key Distinctions Between Equal and Congruent