Properties of Equality
NAME THAT PROPERTY: A=B then A=B
REFLEXIVE PROPERTY
GIVEN -9(2X-3)=63; PROVE X=-2
1.
2.
3.
4.
1. -9(2X-3)=63 *GIVEN*
2. -18X+27=63 *DISTRIBUTIVE*
3.-18X=36 *SUBTRACTION*
4. X=-2 * DIVISION*
WHAT IS THE DEFINITION OF A TRANSVERSAL?
A LINE THAT INTERSECTS TWO OR MORE LINES
ANGLE 1 AND ANGLE 2 ARE A LINEAR PAIR.
ANGLE 1 = 4X+6
ANGLE 2= 5X+3
SOLVE FOR X
X=19
IF PQ+RS=PS AND RS=XY, THEN PQ+XY=PS
NAME THAT PROPERTY
SUBSTITUTION PROPERTY
IF A=B THEN A+C =B+C
ADDITION PROPERTY OF EQUALITY
GIVEN A/-6+2=5' PROVE A=-18
1.
2.
3.
1. A/-6+2=5 *GIVEN*
2. A/-6=3 *SUBTRACTION*
3. A=-18 *MULTIPLICATION*
WHAT IS THE DEFINITION OF CORRESPONDING ANGLES?
ANGLES ON THE SAME SIDE OF THE TRASNVERSAL AND IN THE SAME POSITION
ANGLE 1= (9X+2)
ANGLE 4= 119
ANGLE 1 AND ANGLE 4 ARE ALTERNATE INTERIOR ANGLES
SOLVE FOR X
X=13
IF JK+LM=NP, THEN JK=NP
NAME THAT PROPERTY
IF A(B+C), THEN A(B+C) =AB+BC
DISTRIBUTIVE PROPERTY
5N=42=12N; PROVE N=-6
GIVE REASONING:
1. 5N-42=12N
2.-42=7N
3.-6=N
4.N=-6
1. GIVEN
2. SUBTRACTION
3.DIVISION
4.SYMMETRIC
WHAT IS THE DEFINITION OF ALTERNATE EXTERIOR ANGLES?
EXTERIOR ANGLES, NON-ADJACENT, AND ON OPPOSITE SIDES OF THE TRANSVERSAL
ANGLE 1= 9X+25
ANGLE 2= 13X-19
ANGLE 3= 17Y+5
ANGLE 1 AND ANGLE 2 ARE CORRESPONDING ANGLES.
ANGLE 2 AND ANGLE 3 ARE A LINEAR PAIR
SOLVE FOR X
X=11
IF ANGLE 1 AND ANGLE 2 ARE VERTICAL ANGLES THEN, ANGLE 1 AND ANGLE 2 ARE A VERTICAL ANGLE PAIR.
NAME THAT JUSTIFICATION
DEFINITION OF VERTICAL ANGLES
NAME THAT PROPERTY:
IF 10X+W=41 AND W=1, THEN 10X+1=41
SUBSTITUTION PROPERTY
GIVEN -3(2X+7)=-29; PROVE X=4
1.-3(2X+7)=-29-4X
2. -6X-21=-29-4X
3.-2X-21=-29
4.-2X=-8
5.X=4
1. GIVEN
2. DISTRIBUTIVE
3. ADDITION
4. ADDITION
5. DIVISION
WHAT IS THE DEFINITION OF CONSECUTIVE INTERIOR ANGLES?
INTERIOR ANGLES THAT ARE ON THE SAME SIDE OF THE TRANSVERSAL
ANGLE 1= 6X-7
ANGLE 2=8Y+17
ANGLE 3= 3X-29
ANGLE 1 AND ANGLE 2 ARE A VERTICAL PAIR
ANGLE 1 AND ANGLE 3 ARE CONSECUTIVE INTERIOR
SOLVE FOR X AND Y
X=24
Y=15
MEASURE OF ANGLE ABD + MEASURE OF ANGLE DBC= MEASURE OF ANGLE ABC
NAME THAT REASON
ANGLE ADDITION POSTULATE
NAME THAT PROPERTY:
IF 4W-1=11, THEN 4W=12
ADDITION PROPERTY OF EQUALITY
GIVEN 6X-2Y=14; PROVE Y=3X-7
1.
2.
3.
1. 6X-2Y=14 GIVEN
2.-2Y=-6X+14 SUBTRACTION
3. Y=3X-7 DIVISION
LIST WHETHER THE FOLLOWING ANGLES ARE CONGRUENT OR SUPPLEMENTARY.
1. CORRESPONDING ANGLES
2. ALTERNATE INTERIOR ANGLES
3. ALTERNATE EXTERIOR ANGLES
4. CONSECUTIVE INTERIOR ANGLES
5. LINEAR ANGLES
6. VERTICAL ANGLES
1.CONGRUENT
2. CONGRUENT
3. CONGRUENT
4. SUPPLEMENTARY
5. SUPPLEMENTARY
6. CONGRUENT
ANGLE 1 = 7X+12
ANGLE 2= 12X-28
ANGLE 3= 9Y-77
ANGLE 1 AND ANGLE 2 ARE ALTERNATE INTERIOR ANGLES
ANGLE 2 AND ANGLE 3 FORM A LINEAR PAIR.
SOLVE FOR X AND Y
X=8
Y=21
IF ANGLE 1 AND ANGLE 2 ARE A LINEAR PAIR, THEN ANGLE 1 AND ANGLE 2 ARE SUPPLEMENTARY ANGLES.
NAME THAT REASONING
SUPPLEMENT THEOREM