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Geometry
Properties from Algebra
Match each statement with the appropriate property of equality.
1) If a = b and c ≠ 0, then
2)
3)
4)
5)
6)
7)
a
=
c
then a + c = b + c.
then b = a.
then a ⋅ c = b ⋅ c.
then a − c = b − c.
b
c
.
a) Addition Property
b)
c)
d)
e)
f)
g)
If a = b,
If a = b,
If a = b,
If a = b,
a=a
If a = b and b = c, then a = c.
Subtraction Property
Multiplication Property
Division Property
Reflexive Property
Symmetric Property
Transitive Property
Justify each statement with a property from algebra or definition or postulate from geometry.
8) If AB = CD and BC = BC , then AB + BC = CD + BC
9) If 3m∠1 = 93 then m∠1 = 31
10) BC ≅ BC
11)
If point A is on the interior of ∠XOY , then m∠XOA + m∠AOY = m∠XOY
12)
If m∠1 = m∠3 and m∠ 2 = m∠3, then m∠1 = m∠ 2.
13)
If AB ≅ CD and CD ≅ EF , then AB ≅ EF .
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14) Complete the proof.
D
E
Given: m∠1 = m∠3
Prove: m∠ABE = m∠DBC
1
5.
m∠1 = m∠3
m∠ 2 = m∠2
m∠1 + m∠ 2 = m∠3 + m∠ 2
m∠ABE = m∠1 + m∠ 2
m∠DBC = m∠2 + m∠3
m∠ABE = m∠DBC
3
C
B
A
1.
2.
3.
4.
2
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15) Complete the proof.
D
E
F
B
C
Given: AB = DE , EF = BC
Prove: AC = DF
A
1.
2.
3.
4.
___________________________
AB + BC = DE + EF
AB + BC = AC; DE + EF
AC = DF
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Given
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Answer Key
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
D
A
F
C
B
E
G
Addition Property of =
Division Property of =
Reflexive
Angle Addition Postulate
Substitution
Transitive Property of congruence
Given, Reflexive, Addition Prop. of =, Angle Addition Postulate, Substitution
AB=DE & EF=BC, Addition Prop of =, Segment Addition Postulate, Substitution
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