Geometry – Fall 2014
Name: ________________________
CW # 18
RSN 11: Complete each statement below
Name of Property of Equality
Definition
Reflexive Property of Equality
a=
Symmetric Property of Equality
if a = b, then
Transitive Property of Equality
if a = b and b = c, then
Addition Property of Equality
if a = b, then a + c =
Subtraction Property of Equality
if a = b, then a - c =
Multiplication Property of Equality
if a = b, then a • c =
Division Property of Equality
if a = b, then a/c =
Distributive Property of Equality
if a(b + c), then
Substitution Property of Equality
if a + b = c and b = f, then
RSN 12: Fill in the blanks and/or complete the two column Algebraic proof. Provide a reason for each step.
Given: 60 – 2x = 18x
Given: -4( x + 2 ) = -5x
Prove: x = 3
Prove: x = 8
Statements
Reasons
Statements
Reasons
1.
60 – 2x = 18x
1. ________________
1. ________________
1. Given
2.
60 = 20x
2. _________________
2. _________________
2. Distributive P. of =ity
3.
3=x
3. ________________
3. ________________
3. Addition P. of =ity
4.
x=3
4. _________________
4. _________________
4. Division P of =ity
5. _________________
5. Symmetric P of =ity
Given: 34 – 3x = 5(x + 2)
Given: 10 = 2(5 – 2x)
Prove: x = 3
Prove: x = 0
Statements
1.
Reasons
1.
Statements
1.
Reasons
1.
RSN 13: Fill in the blanks accurately for the proofs of the overlap theorems below.
Two different approaches were used in the proofs, yet each approach will work for both
theorems.
Segment Overlap Theorem
Given:
AB = CD (mark this on the drawing below)
●
●
AC = BD
A
B
Prove:
STATEMENT
●
C
●
D
REASON
1. ____________________
1. Given
2. BC = BC
2. _______________ Property of Equality
3. AB + BC = BC + CD
3. _______________ Property of Equality (steps __ & __)
4. AB + BC = AC
4. _______________________ Postulate (diagram)
5. _____ + ______ = BD
5. _______________________ Postulate (diagram)
6. _____________
6. Substitution Property of Equality
(steps ____ & ____ in for step ____)
Q.E.D.
Angle Overlap Theorem
Given:
m  MAC = m  PAT
Prove:
m  CAP = m  TAM
C ●
●M
P●
A ●
STATEMENT
●
T
REASON
1. m  MAC = m  PAT
1. ________________
2. m  MAC + m  MAP = m  CAP
2. __________________________ Postulate
3. m  PAT + m  MAP = m  TAM
3. __________________________ Postulate
4. m  _______ + m  MAP = m  TAM
4. Substitution Property of Equality (steps 1 and 3)
5. m  ________ = m  ________
5. ________________________ (steps ____ & ____)
Q.E.D.