Geometry
2.5 Notes
(2.5) Reason Using Properties from Algebra
Objective: Use algebra to make logical arguments
Do Now:
Solve each equation:
1). 6x + 2 = -3x - 16
2). –4(x – 8) = -16
Solve P = 2l + 2w for w
4). When you are asked to solve an equation, what does it mean?
When solving an equation you use properties of real numbers.
Segment lengths and angle measures are real numbers, which means:
Algebraic Properties of Equality
Let a, b and c be real numbers (notation: a,b,c ∈ ℜ )
Property of Equality
Conditional statement
Addition Property
If a = b, then
Subtraction Property
If a = b, then
Multiplication Property
If a = b, then
Division Property
If a = b, then
Substitution Property
If a = b, then
Example 1 Justify each step
a). Solve 2x – 5 = 11. Write the reason for each step
Equation
Reason
Mrs. Poyner
In words
Explanation
page 1
Geometry
2.5 Notes
Example 1 Justify each step (continued)
b). Solve 3x + 8 = -4x – 34. Write the reason for each step
Reason
Equation
Explanation
Let a, b and c be real numbers (notation: a,b,c ∈ ℜ )
Distributive Property
a(b + c) =
Example 2 Use the Distributive Property
Solve 60 = -3(8x – 4). Justify your steps.
Equation
Reason
Example 3 Use properties in the real world
The cost C of using a certain cell phone can be modeled by the plan rate formula C = 0.30(m – 300) + 39.99,
where m represents the number of minutes over 300. Solve the formula for m. Justify your steps.
Equation
Reason
Mrs. Poyner
page 2
Geometry
2.5 Notes
Some properties that will be use often this year:
Reflexive Property of Equality
Real numbers
For any real number a
Segment lengths
For any segment AB
Angle measures
For any angle A
a=a
Symmetric Property of Equality
Real numbers
For any real numbers a and b
Segment lengths
For any segments AB and CD
Angle measures
For any angles A and B
If a = b, then b = a
Transitive Property of Equality
Real numbers
For any real numbers a, b, and c
Segment lengths
For any segments AB, CD, and EF
Angle measure
For any angles A, B and C
If a = b and b = c, then a = c
Example 4
In the diagram m ∠ ABD=m ∠ CBE. Show that m ∠ 1=m ∠ 2. Justify your steps.
Equation
Reason
A
1
Explanation
B
C
2
3
D
E
Example 5
The city is planning to add two stations between the beginning and the end of a commuter train line. Use
the information given. Determine whether RU = TU.
Reason
Equation
Explanation
R
Mrs. Poyner
S
page 3
T
U