Symmetric Property of Equahty
2.4 – Homework
me
ESthe property of equahty or congruence ihustrated.
For more practice, see Extra Practice.
C^ = XY
f m^A = 45 and 45 = m/LB , then mAA = mAB.
in the reason that justifies each step.
Problem Fill
Solving
1, Solve for x.
Example
Algebra Fill in the reason that justifies each step.
Statements
1 and 2
Reasons
1. Solve
for x.= 180
m∠CDE
+ m∠EDF
page 90)
a.
(3x + 20)°
mACDE + m/LEDF = 180
a.
C
D
For
more practice,
see Extra Prac
b.
X + (3x + 20) = 180
x + (3x + 20) = 180 b.
ving
4x + 20 = 180
c.
Ax = 160
d.
X = 40
e.
4x + 20 = 180 c.
gebra Fill in the reason that justifies each step.
3{n + 4)
2. Solve for n.
Solve for x.
4x = 160 d.
Given: ^
= 42
X
mACDE + m/LEDF
= 180
XZ + ZY
= XY
a. ?
a.
x = 40 e.
3(n ++ 20)
4) + =
3n 180
= 42
X + (3x
3?7 + 12 + 3« = 42
4x + 20 = 180
2, Solve for n.
6n + 12 = 42
Given: XY = 42
Ax =
160
6n = 30
StatementsX =n 40
= 5
XZ + ZY = XY a.
(3x + 20)°
D
b.
b.
c.J_
c.
d. JL
d.
e.^
Reasons
f.e. ?
+ 4) in Algebra
3n
Lesson 2-4 3{n
Reasoning
Solve for n.
Given: ^
C
3n
3(n + 3) + 3n = 42 b.
= 42
XZ + ZY = XY
3n + 12 + 3n = 42 c.
3(n + 4) + 3n = 42
X
a.
?
b.
3?7 + 12 + 3« =6n 42
+ 12 = 42 d.
c.J_
6n + 12 = 42
d. JL
6n = 30
6n
= 30
n = 5
n=5
e.
f.
e.^
f.
?
Lesson 2-4
Reasoning in Algebra
91
Give a reason for each step.
3.
Statements
1
x − 5 = 10
2
Reasons
a.
"1
%
2 $ x − 5' = 20
#2
&
b.
x −10 = 20
c.
x = 30
d.
4.
Statements
5 ( x + 3) = −4
a.
5x +15 = −4
b.
5x = −19
c.
19
5
d.
x=−
Reasons
Name the property that justifies each statement.
5. ∠Z ≅ ∠Z
6. 2 (3x + 5) = 6x +10
7. If 12x = 84, then x = 7.
8. If ST ≅ QR , then QR ≅ ST
9. If m∠A = 15 , then 3m∠A = 45
10. XY = XY
11. If 3x + 14 = 80, then 3x = 66.
12. If KL = MN, then MN = KL.
13. If 2x + y = 5 and x = y, then 2x + x = 5.
14. If AB – BC = 12, then AB = 12 + BC.
15. If ∠1 ≅ ∠2 and ∠2 ≅ ∠3 , then ∠1 ≅ ∠3 .
Use the given property to complete each statement.
16. Addition Property of Equality
If 2x – 5 = 10, then 2x = __________.
17. Subtraction Property of Equality
If 5x + 6 = 21, then __________ = 15.
18. Symmetric Property of Equality
If AB = YU, then __________.
19. Symmetric Property of Congruence
If ∠H ≅ ∠K , then __________ ≅ ∠H .
20. Reflexive Property of Congruence
∠PQR ≅ __________
21. Distributive Property
3(x – 1) = 3x - __________
22. Substitution Property
If LM = 7 and EF + LM = NP, then __________ = NP.
23. Transitive Property of Congruence
If ∠XYZ ≅ ∠AOB and ∠AOB ≅ ∠WYT , then __________.
24. Multiplication Property of Equality
If
^
1
TR = UW , then __________.
3
25. Fill in the reason that justifies each step.
27. Algebra
in the
reason
AD .justifies each step.
Given: CFill
is the
midpoint
ofthat
Given: C is the midpoint of AD.
Statements
CC is
AD.a.
is the
the midpoint
midpoint ofofAD
4x
2x + 12
Reasons
D
a.
AC = CD
b.
4x =2x + 12
c.
AC = CD b.
2x = 12
d.
= 6
Algebra FillX in
the reason that justifies each step.
e.
4x = 2x + 12 c.
In the figure at the right, KM
Given: 28.
C isAlgebra
the midpoint
of AD.
g
C
28,
is the
2x-5
= 35.
a. Solve for x. Justify each step.
b. Find theoflength
midpoint
AD.of KL. a.
4x 2x
K
2x + 12
M
D
2x = 12 d.
AC = CD
b.
X' 29. Algebra In the figure at the right, m/I GF7 = 128.
c.
4x =2x +a. 12
Solve for x. Justify each step.
(9x - 2)°
X = 6 e.
2x = 12 b. Find m/LEFI.
d.
e.
X = 6
30. Algebra Fill in the reason that justifies each step.
Given:
bisects
^ABD.
26.
In theBC
figure
at the
right, KM = 35.
Algebra In
the figure
at the
right, KM = 35.
^Cx.bisects
Z^ABD. step.
a.
a. Solve for
Justify
a. Solve
for xeach
. Justify each step.
=ofmACBD
b.Reasons
Statements
length
KL.
b. Find them/LABC
a. 6n + 1 = 4n + 19
a.
c.
2n = 18
Algebra In the figure at the right, m/I GF7 = 128.
e.
n = 9
a. Solve for
b. x. Justify each step.
b.
d.
2x-5
K
M
(4« + 19)
(9x - 2)°
Error Analysis The steps below "show" that 1 = 2. Find the error.
enge
b. Find 31.
m/LEFI.
c.Given: a = b
c.
Algebra Fill in the
reason that justifies
each step.
Given
a = b
ah = 52
Given: BC
d. bisects ^ABD.
a2 = b^-a^
Multiplication Property of Equality
d.
Subtraction Property of Equality
^C bisects Z^ABD.
a.
a) = {b + a) {b - a)
Distributive Property
a = b
m/LABC = mACBD
Division Property of Equahty
e.
a
=
+ a
a +
6n + 1 = 4n + 19
e.
b.
Substitution Property
a
c.
2x
h
ding
ise 28,
allenge
X'
Landers,
ers
Fourth
em
y as"
rs.
K
29. Algebra In the figure at the right, m/I GF7 = 128.
a.a. Solve
Solvefor
forx.x.Justify
Justify each
eachstep.
step.
a.
b. Statements
Find m/LEFI.
M
(9x - 2)°
Reasons
a.
30. Algebra Fill in the reason that justifies each step.
b.
Given: BC bisects ^ABD.
b.
^C bisects Z^ABD.
c.
a.
m/LABC
= mACBD
b. justifies
^ 27. Algebra
Fill in the reason that
c.
6n + 1Given:
= 4nC+is the
19 midpoint ofc.
AD.
2nC=is the
18 midpoint of AD.
d.
d.
nAC
= =9 CD
4x =2x + 12
d.
e.
each step.
4x
2x + 12
(4« + 19)
D
a.
b.
c.
31. Error Analysis
The steps below "show"
that 1 = 2. Find the error.
2x = 12
d.
e.
e.
X = 6
Given: a = b
nd solving Exercise 28,
e p. 95.
dge,
2x
27. In the figure at the right, ∠GFI = 128 .
e.
28. Algebra In the figure at the right, KM = 35.
Given
a = b
Reading Math
a. Solve for x. Justify each step.
.52the length of KL.
or help with reading b. Find m∠EFI
Multiplication
ahb. =
Find
nection
2x-5
28. Algebra In the figure at the right, KM = 35.
a. Solve for x. Justify each step.
b. Find the length of KL.
X'
a2 = b^-a^
2x-5
K
b. Find m/LEFI.
= b + a
M
Property of Equality
Subtraction Property of Equality
29. Algebra In the figure at the right, m/I GF7 = 128.
a)a. =Solve
{b for
+ a)
{b - a)
x. Justify
each step.Distributive Property
a
2x
(9x - 2)°
Division Property of Equahty
Property
= a + Fill
a in the reason thatSubstitution
30. aAlgebra
justifies each step.
28. Fill in the reason that justifies each step.
aGiven:
= 2aBC
bisects ^ABD.
Simplify.

Division
Property of Equality
1^C= bisects
2
a.
∠ABDZ^ABD.
Given: BC bisects
.
m/LABC = mACBD
b.
Statements
Reasons

Relationships
You
know
that
the
relationships
"is equal to" and "is congruent to'
6n + 1 = 4n a.
+ 19
c.
a. BC bisects ∠ABD
+ that
19) this is
are reflexive, symmetric,
In a later chapter, you will(4«see
2n = 18 and transitive.
d.
also true for the relationship
"is similare. to." Consider the following relationships
n = 9
State whether
each relationship is reflexive,symmetric, transitive,
b.among
b.
m∠ABCpeople.
= m∠CBD
Challenge
31. Error Analysis The steps below "show" that 1 = 2. Find the error.
or none of these.
Given: a = b
Sample: The relationship "is younger than" is transitive. If Sue is younger
Given
a = b c.
c. 6n + 1 = 4n + 19
than Fred and Fred
is
younger
than
Alana,
then Sue is younger than Alana.
Multiplication Property of Equality
ah = 52
The relationship "is younger than" is not reflexive because Sue is not younger
a2 = b^-a^
Subtraction Property of Equality
because if Property
Sue is younger than Fred,
than herself. It is also not symmetric Distributive
a) = {bd.+ a) {b - a)
d. 2n = 18
Fred is not younger than Sue.
a
= b + a
a
= a + as
a
32. has the same birthday
e. n = 9
a = 2ae.
34. hves in the same state as
1 = 2
36. is the same height as
Division Property of Equahty
Substitution
Property
33. is taller
than
Simplify.
35. lives in a different state than
Division Property of Equality
37. is a descendant of
Answer Key
1.
2.
Statements
m∠CDE + m∠EDF = 180
x + (3x + 20) = 180
4x + 20 = 180
4x = 160
x = 40
Statements
XZ + ZY = XY
3(n + 3) + 3n = 42
3n + 12 + 3n = 42
6n + 12 = 42
6n = 30
n=5
3.
Reasons
a. Angle Addition Postulate
b. Substitution Property
c. Simplify
d. Subtraction Property of Equality
e. Division Property of Equality
Reasons
a. Segment Addition Postulate
b. Substitution Property
c. Distributive Property
d. Simplify
e. Subtraction Property of Equality
f. Division Property of Equality
Statements
Reasons
1
x − 5 = 10
2
"1
%
2 $ x − 5' = 20
#2
&
x −10 = 20
x = 30
4.
a. Given
b. Multiplication Property of
Equality
c. Distributive Property
d. Addition Property of Equality
Statements
Reasons
5 ( x + 3) = −4
5x +15 = −4
a. Given
b. Distributive Property
5x = −19 c. Subtraction Property of Equality
19 d. Division Property of Equality
x=−
5
5. Reflexive Property of Congruence
6. Distributive Property
7. Division Property of Equality
8. Symmetric Property of Congruence
9. Multiplication Property of Equality
10; Reflexive Property of Equality
11. Subtraction Property of Equality
12. Symmetric Property of Equality
13. Substitution Property
14. Addition Property of Equality
15. Transitive Property of Equality
16. 15
17. 5x
18. YU = AB
19. ∠K
20. ∠PQR
21. 3
22. EF + 7
23. ∠XYZ ≅ ∠WYT
24. TR = 3UW
25.
Statements
C is the midpoint of AD
AC = CD
4x = 2x + 12
2x = 12
X=6
26.
Statements
a. KL + LM = KM
b. 2x – 5 + 2x = 35
c. 4x – 5 = 35
d. 4x = 40
e. x = 10
Reasons
a. Given
b. Definition of a midpoint
c. Substitution Property of Equality
d. Subtraction Property of Equality
e. Division Property of Equality
Reasons
a. Segment Addition Postulate
b. Substitution Property
c. Simplify
d. Addition Property of Equality
e. Division Property of Equality
27. a.
Statements
a. m∠GFE + m∠EFI = m∠GFI
b. 9x – 2 + 4x = 128
Reasons
a. Angle Addition Postulate
b. Substitution Property
c. 13x – 2 = 128
d. 13x = 130
c. Simplify
d. Addition Property of Equality
e. x = 10
e. Division Property of Equality
b. 40
28.
Statements

a. BC bisects ∠ABD
b. m∠ABC = m∠CBD
c. 6n + 1 = 4n + 19
d. 2n = 18
e. n = 9
Reasons
a. Given
b. Definition of an Angle Bisector
c. Substitution Property
d. Subtraction Property of Equality
e. Division Property of Equality