2.5 - Reasoning in Algebra

2.5 - Reasoning in Algebra

by Steve Dull

​Today's Objective:

​

To connect reasoning in algebra and geometry.

​

​In geometry we accept postulates and properties to be true. Some of the properties we accept to be true are the properties of equality from algebra.

​

​You'll want to take a moment to write these down, either in your fillable notes (in class) or your notebook (remote).

​And one more:

​

​Let's look at an example:

​

​Now you try #1 on your notes:

​Some of the properties of equality have corresponding properties of congruence:

​

​How can you tell the difference?

Fill in the Blanks

Which property justifies going from the first statement to the second statement?

$\angle O\cong\angle W\ and\ \angle W\cong\angle L$  

$\angle O\cong\angle L$  

Fill in the Blanks

Which property justifies going from the first statement to the second statement?

$3\left(x+5\right)=9$  

$3x+15=9$  

​Proofs

​A proof is a convincing argument that uses deductive reasoning. A proof logically shows why a conjecture is true.

​

​A two-column proof lists each statement on the left and the justification, or reason, on the right. Each statement follows logically from the steps before it.

​

​Your last statement is what you want to prove.

​

​

​

​

​Today we will practice proving algebraic equations. Complete the algebraic proofs on the notes handout, then you can work on the 2.5 assignment in MathXL.

​

In the next section we will use what we have learned to prove geometric statements.