NAME THE PROPERTY OF EQUALITY AND CONGRUENCE
Reflexive Property
|
Equality AB = AB m∠A = m∠A |
Congruence AB ≅ AB ∠A ≅ ∠A |
Symmetric Property
|
Equality If AB = CD, then CD = AB. If m∠A = m∠B, then m∠B = m∠A. |
Congruence If AB ≅ CD, then CD ≅ AB. If ∠A ≅ ∠B, then ∠B ≅ ∠A. |
Transitive Property
Equality
If AB = CD and CD = EF, then AB = EF.
If m∠A = m∠B and m∠B = m∠C, then m∠A = m∠C.
Congruence
If AB ≅ CD and CD ≅ EF, then AB ≅ EF.
If ∠A ≅ ∠B and ∠B ≅ ∠C, then ∠A ≅ ∠C.
PROPERTIES OF EQUALITY
Addition Property
Adding the same number to each side of an equation produces an equivalent equation.
Example
x - 3 = 7
x - 3 + 3 = 7 + 3
Subtraction Property
Subtracting the same number from each side of an equation produces an equivalent equation.
Example
y + 5 = 11
y + 5 - 5 = 11 - 5
Multiplication Property
Multiplying each side of an equation by the same nonzero number produces an equivalent equation.
Example
Division Property
Dividing each side of an equation by the same nonzero number produces an equivalent equation.
Example
Substitution Property
Substituting a number for a variable in an equation produces an equivalent equation.
Example
x = 7
2x + 4 = 2(7) + 4
Problem 1 :
Match the statement with the property it illustrates.
|
1. m∠DEF = m∠DEF 2. If PQ = ST, then ST = PQ. 3. XY = XY 4. If ∠J ≅ ∠K and ∠K ≅ ∠L, then ∠J ≅ ∠L. 5. If PQ = QR and QR = RS, then PQ = RS. 6. If m∠X = m∠Y, then m∠Y = m∠X. |
A. Symmetric Property of Equality B. Reflexive Property of Equality C. Transitive Property of Equality D. Reflexive Property of Congruence E. Symmetric Property of Congruence F. Transitive Property of Congruence |
Solution:
|
1. m∠DEF = m∠DEF |
B. Reflexive Property of Equality |
|
2. If PQ = ST, then ST = PQ. |
E. Symmetric Property of Congruence |
|
3. XY = XY |
D. Reflexive Property of Congruence |
|
4. If ∠J ≅ ∠K and ∠K ≅ ∠L, then ∠J ≅ ∠L. |
F. Transitive Property of Congruence |
|
5. If PQ = QR and QR = RS, then PQ = RS. |
C. Transitive Property of Equality |
|
6. If m∠X = m∠Y, then m∠Y = m∠X. |
A. Symmetric Property of Equality |
Problem 2 :
Completing statements use the property to complete the statement.
1. Reflexive Property of Equality: JK = ____
JK = JK
2. Symmetric Property of Equality: If m∠P = m∠Q, then ___ = __.
If m∠P = m∠Q, then m∠Q = m∠P
3. Transitive Property of Equality: If AB = BC and BC = CD, then ___ = ___.
If AB = BC and BC = CD, then AB = CD
4. Reflexive Property of Congruence: ___ ≅ ∠GHJ
∠GHJ ≅ ∠GHJ
5. Symmetric Property of Congruence: If ___ ≅ ___, then ∠XYZ ≅ ∠ABC.
If ∠ABC ≅ ∠XYZ, then ∠XYZ ≅ ∠ABC
6. Transitive Property of Congruence: If GH ≅ IJ and ___ ≅ ___, then GH ≅ PQ.
If GH ≅ IJ and IJ ≅ PQ, then GH ≅ PQ
Problem 3 :
Use each property of equality or congruence to complete each statement
1. Symmetric Property:
If ∠DEF ≅ ∠GHI, then
Solution :
By applying symmetric property, if a = b then b = a
If ∠DEF ≅ ∠GHI, then ∠GHI ≅ ∠DEF
2. Transitive Property:
If AB + CD = EF and EF = GH, then
Solution :
By applying transitive property, if a = b, b = c then a = c.
AB + CD = EF -----(1)
EF = GH ------(2)
AB + CD = GH
3. Substitution Property:
If m∠1 - m∠2 = 90 and m∠2 = m∠4, then
Solution :
m∠1 - m∠2 = 90 ----(1)
m∠2 = m∠4----(2)
By applying (2) in (1), we get
m∠1 - m∠4 = 90
4. Reflexive Property:
m∠WXY = ?
Solution :
Using reflexive property, if a = a, then b = b
m∠WXY
5. Addition Property:
If MN = RS and AB = CD, then
Solution :
MN = RS -----(1)
AB = CD -----(2)
(1) + (2)
MN + AB and RS + CD
6. Subtraction Property:
If m∠1 + 45 = m∠S + 45, then
Solution :
m∠1 + m∠S
7. Multiplication Property:
If (1/5)CD = 15, then
Solution :
(1/5) CD ⋅ 5 = 15 ⋅ 5
CD = 75
8. Division Property:
If 3m∠JKL = 99, then
Solution :
Using division property, dividing by 3 on both sides.
3m∠JKL/3 = 99/3
m∠JKL = 33
9. Symmetric Property:
If AB = YU, then
Solution :
Using symmetric property, if a = b then b = a
If AB = YU, then YU = AB
10. Symmetric Property:
If ∠H = ∠K, then
Solution :
Using symmetric property, if a = b then b = a
∠K ≅ ∠H.
11. Reflexive Property:
∠PQR ≅ ∠PQR
12. Distributive Property:
3(x - 1)
Solution :
Using distributive property, distributing 3, we get
= 3x - 3
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