2.4. Algebraic and Congruence Properties http://www.ck12.org
2.4 Algebraic and Congruence Properties
Learning Objectives
- Understand basic properties of equality and congruence.
- Solve equations and justify each step in the solution.
- Use a 2-column format to prove theorems.
Review Queue
Solve the following problems.
1.Explainhow you would solve 2x− 3 =9.
2.If two angles are a linear pair, they are supplementary.
If two angles are supplementary, their sum is 180 ◦.
What can you conclude? By which law?
- Draw a picture with the following:
(^6) LMNis bisected byMO LM∼=MP
(^6) OMPis bisected byMN Nis the midpoint ofMQ
Know What?Three identical triplets are sitting next to each other. The oldest is Sara and she always tells the truth.
The next oldest is Sue and she always lies. Sally is the youngest of the three. She sometimes lies and sometimes
tells the truth.
Scott came over one day and didn’t know who was who, so he asked each of them one question. Scott asked the
sister that was sitting on the left, “Which sister is in the middle?” and the answer he received was, “That’s Sara.”
Scott then asked the sister in the middle, “What is your name?” The response given was, “I’m Sally.” Scott turned to
the sister on the right and asked, “Who is in the middle?” The sister then replied, “She is Sue.” Who was who?
Properties of Equality
Recall from Chapter 1 that the = sign and the word “equality” are used with numbers.
The basic properties of equality were introduced to you in Algebra I. Here they are again:
Forallrealnumbersa,b,andc:
TABLE2.13:
Examples
Reflexive Property of Equality a=a 25 = 25
Symmetric Property of Equality a=bandb=a m^6 P= 90 ◦or 90◦=m^6 P