Download Notes: 2-5 Reasoning in Algebra and Geometry

Notes: 2-5 Reasoning in Algebra and Geometry Name_____________________ Date_______ Per__
Property
Symbols
Symmetric Property of Equality
Words
You can ________ the same number to
each side of an equation
You can __________ the same number
from each side of an equation.
You can ___________ by the same number
on each side of an equation.
You can __________ each side an
equation by the same number.
You can ______________ a part of an
expression with an equivalent value.
Any value is __________ to itself.
Any geometric object is ___________ to
itself.
You can change the order of an
____________
Symmetric Property of Congruence
You can change the order of a
_____________
If Q  R, then R  Q.
statement.
Addition Property
Subtraction Property
Multiplication Property
Division Property
Substitution
Reflexive Property of Equality
Reflexive Property of Congruence
Transitive Property of Equality
Transitive Property of Congruence

If x = 2, then x + 2 = 4.
If y = 8, then y – 3 = 5.
If z = 2, then 5z = 10.
If 6m = 12, then m = 2.
If 3x + 5 = 3 and x = 2, then 3(2) + 5 = 3.
AB = AB
Z  Z
If XY = ZA, then ZA = XY
If two values are _________ to a third
If KL = MN and MN = TR, then KL = TR
value, then they are equal to each other.
If two values are congruent to a third
If 1  2, and 2  3, then 1  3
value, then they are ________________ to
each other.
Remember: Distributive Property!!! _____________________________________________________
Fill in the reason that justifies each step.
1. 0.25x + 2x + 12 = 39
2.25x + 12 = 39
2.25x = 27
225x = 2700
x = 12
Given
a.
b.
c.
d.
2. Given: mABC = 80
mABD  3x  3 , mCBD  6 x  5 , mABC = 80
Given
mABD + mDBC = mABC
Angle Addition Postulate
(3x + 3) + (6x + 5) = 80
Substitution Property
9x + 8 = 80
a.
9x = 72
b.
x=8
c.
A ___________ is an argument that uses deductive reasoning to show why something is true.
A _________________ proof is one type of proof. Each statement is on the left, and your justification, or reason,
is on the right. A reason may be a ____________, ______________, ______________, or ______________,.
A list of properties is on page 841. A list of postulates and theorems starts on page 842. Use these pages as a
reference!
Ex: Write the reasons for this two-column proof.
Given: QWT and TWX are complementary.
Prove: x = 28
Statements
Reasons
1) QWT and TWX are complementary
1)
mQWT  2 x , mXWT  x  6
2) mQWT + mTWX = 90
2)
3) 2x + x + 6 = 90
3)
4) 3x + 6 = 90
4)
5) 3x = 84
5)
6) x = 28
6)
Ex: Fill in the missing statements or reasons for the two-column proof.
Given: E is the midpoint of DF .
Prove: DE = 23
Statements
1) E is the midpoint of DF .
DE  6 x  4 , EF  8 x  1
2)
Reasons
1)
2) Definition of midpoint
3) 6x + 5 = 8x – 1
3)
4) 5 = 2x – 1
4)
5)
5) Addition Property of Equality
6)
6) Division Property of Equality
7) DE = 6(3) + 5
7)
8) DE = 23
8)