2-5 Reasoning in Algebra and Geometry

Properties of Equality

The Distributive Property

Problem 1: Justifying Steps when Solving an Equation

What is the value of x? Justify each step

1) 180

2)2 30 180

3)3 30 180

4)3 150

5) 50

AOM MOC

x x

x

x

x

Problem 1: Justifying Steps when Solving an Equation

What is the value of x? Justify each step

1) 2 75

2) 75

3) 75

x x

x

x

Properties of Congruence

Problem 2: Using Properties of Equality and Congruence

What is the name of the property of equality or congruence that justifies going from the 1st statement to the second statement?

What is the name of the property of equality or congruence that justifies going from the 1st statement to the second statement?

What is the name of the property of equality or congruence that justifies going from the 1st statement to the second statement?

Proof: a convincing argument that uses deductive reasoning (shows why a conjecture is true)

Two-Column Proof: lists each statement on the left and the justification or reason for each statement on the right. Each step must follow logically from the steps before it.

Problem 3: Writing a Two-Column Proof

1) 1 3

2) 2 2

3) 1 2 3 2

4) 1 2

3 2

5)

m m

m m

m m m m

m m AEC

m m DEB

m AEC m DEB

1)

2)

3)

4)

5)

6)

7)

AB CD

AB CD

BC BC

AB BC BC CD

AB BC AC

BC CD BD

AC BC

AC BC