REASONING WITH PROPERTIES FROM ALGEBRA

1
REASONING WITH PROPERTIES FROM ALGEBRA

• GOALS
• TO USE PROPERTIES FROM ALGEBRA
• TO USE PROPERTIES OF CONGRUENCE

2
ALGEBRA PROPERTIES OF EQUALITIES

• ADDITION PROP IF AB THEN AC BC
• SUBTRACTION PROP IF AB THEN A-C B-C
• MULTIPLICATION PROP IF AB THEN AC BC

3
DIVISION PROP IF AB AND C0 THEN A C B C

• REFLEXIVE PROP FOR ANY REAL NUMBER A, AA
• SYMMETRIC PROP IF AB THEN BA
• TRANSITIVE PROP IF AB AND BC THEN AC

4

• SUBSTITUTION PROP IF AB, THEN A MAY BE
  SUBSTITUTED FOR B IN ANY EQUATION OR EXPRESSION
• SEGMENT NAMES AND ANGLES CAN BE SUBSTITUTED FOR
  VARIABLES.

5
PROPERTIES OF CONGRUENCE

• REFLEXIVE ANY GEOMETRIC OBJECT IS CONGRUENT TO
  ITSELF
• SYMMETRIC IF ONE GEOMETRIC OBJECT IS CONGRUENT
  TO A SECOND, THEN THE SECOND OBJECT IS CONRUENT
  TO THE FIRST

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PROPERTIES OF CONGRUENCE

• TRANSITIVE IF ONE GEOMETRIC OBJECT IS CONGRUENT
  TO A SECOND, AND THE SECOND IS CONGRUENT TO A
  THRID, THEN THE FIRST OBJECT IS CONGRUENT TO THE
  THRID.

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PROOFS

• WRITTEN GEOMETRIC ARGUMENT
• 3 STYLES FLOW CHART, PARAGRAPH OR MOST COMMON
  2-COLUMN
• EVERY STEP IN ANY PROOF MUST BE EITHER GIVEN
  INFORMATION OR JUSTIFIED BY A DEFINITION, AN
  ALGEBRAIC PROP, A POSTULATE, OR A THEOREM.

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EXAMPLE

• GIVEN mltAOC500, LET lt1ltAOB lt2ltBOC mlt1250
• PROVE OB BISECTS ltAOC

C
B
2
O
1
A