Notes – Lesson 2.4
Geometry
Name _________________________________________
Justifications for doing Algebra Problems
Addition Property of Equality
- the same number is added to both sides.
x – 8 = 10
Subtraction Property of Equality
- the same number is subtracted from both sides
x+2=5
Multiplication Property of Equality
- the same number is multiplied to both sides
Division Property of Equality
- the same number is being divided by to both sides
x
 10
4
10x = 60
Distributive Property
- an expression of the form a(b + c) is equal to ab + ac
5(a + 6)
Give a reason for each step.
1)
1. 2x – 4 = 10
1. ______________________
2)
1. 0.25x + 2x + 12 = 39
1. ________________
2. 2x = 14
2. ______________________
2. 2.25x + 12 = 39
2. ________________
3. x = 7
3. _____________________
3.
3. ________________
2.25x = 27
4. x = 12
3)
1. 2(x – 5) + 12 = 26
1. ____________________
2. 2x – 10 + 12 = 26
2. ___________________
3. 2x + 2 = 26
3. ____________________
4. 2x = 24
4. ____________________
5. x = 12
5. ___________________
4. ________________
More Justifications.
Segment Addition
- adding 2 segments to make one larger segment
Angle Addition
- adding two angles to make one larger angle
Substitution Property
- if values are equal, one may be substituted for the other (replace)
4) Given: ∠AOC = 139
5) Given:
LM bisects ∠KLN
1. ∠AOC = 139
2. ∠AOB + ∠BOC = ∠AOC
1. ____________________
2. ____________________
1. LM bisects ∠KLN
2. ∠KLM ≅ ∠MLN
1. _____________________
2. ______________________
3. x + 2x + 10 = 139
3. ____________________
3. 2x + 40 = 4x
3. _______________________
4. 3x + 10 = 139
4. _____________________
4. 40 = 2x
4. _______________________
5. 3x = 129
5. ___________________
5. x = 20
5. _______________________
6. x = 43
6. __________________
6) Given: KL is three times as
long as PM.
1. KL = 3(PM)
1. _______________________
2. 5x = 3 _______
2. ________________________
3. 5x = ______
3. ________________________
4. _____ = -12
4. ______________________
5. x = ______
5. _______________________
7) Given: AC = 21
8)
1. AC = 21
1. ________________________
2. AB + BC = AC
2. ________________________
1. ∠QWT + ∠TWX = 90 1. ______________________
3. 2y + (3y – 9) = 21
3. _______________________
2. 2x + (x + 6) =_____
2. ______________________
4. 5y – 9 = 21
4. _______________________
3. ______ + 6 = 90
3. ______________________
5. 5y = 30
5. _______________________
4. _______ = ________ 4. ______________________
6. y = 6
6. _______________________
5. x = ______
More Justifications
Reflexive Property
Symmetric Property
-
Transitive Property
- If a = b and b = c, then a = c.
Example.
If
ABC  SYX and SYX  RST , then ___________________________
Name the property that justifies each statement.
9) If ∠G = 35 and ∠S = 35, then ∠G ≅∠S. _____________________________________
10) If 10x + 6y = 14 and x = 2y, then 10(2y) + 6y = 14 ____________________________
11) If TR = MN and MN = VW, then TR = VW _________________________________
12) If JK = LM, then LM = JK ______________________________________________
13) If ∠Q ≅∠S and ∠S ≅ ∠P, then ∠Q ≅ ∠P ___________________________________
5. ______________________