Download Reasoning in Geometry: Writing Algebraic Proofs

Daily Warm Up Quiz
I. Complete each theorem below:
1. Vertical angles are ________________________________
2. Linear pairs of angles are ____________________________
3. If two angles are congruent and supplementary, then ________
_______________________________________________ .
II. Define:
Complementary
angle:___________________________________
Supplementary angle;
___________________________________
13
15
17
19
III. Given the following diagram, name
A. All linear pairs of angles ____________________________
B. All vertical angle pairs ____________________________
Mrs. McConaughy
Geometry
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Introduction to Proof, Part 1
During this lesson, you will:
 Identify premises for
geometric argument
 Write simple proofs using
Properties of Algebra &
Properties of Equality
Mrs. McConaughy
Geometry
2
Premises for Geometric Proof
1. Definitions and undefined terms
2. Properties of algebra, equality, and
congruence
3. Postulates of geometry
4. Previously accepted or proven geometric
theorems
Mrs. McConaughy
Geometry
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Matching Review: Properties of
Algebra
Column A
a Commutative Property
__
Column B
a. a + b = b + a
of Addition
b. (a + b) + c = a + (b + c)
d
__ Commutative Property
c. (ab)c = a(bc)
of Multiplication
d. ab = ba
b
__ Associative Property of e. a (b + c) = ab + ac
Addition
c
__ Associative Property of
Multiplication
e
__Distributive
Property
Mrs. McConaughy
Geometry
4
Matching Review: Properties of
Equality
1.
__Reflexive
Property of
Equality
2.
__Symmetric Property of
Equality
3.
__Addition Property of
Equality
5.
__Subtraction Property of
Equality
4.
__Multiplication Property
of Equality
6.
__Division
Property of
Equality
Mrs. McConaughy
1. a = a
2. If a = b then b = a.
3. If a = b, then
a+c=b+c
4. If a = b, then
a*c=b*c
5. If a = b, then
a-c=b–c
6. If a = b, then
a / c = b / c (provided c
≠ 0)
Geometry
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Writing Simple Algebraic Proofs Using
Properties of Algebra & Equality
You use properties of algebra and
equality to solve equations. When you
solve an equation, you are writing an
algebraic proof. Each step can be
supported by a property.
Mrs. McConaughy
Geometry
6
Example A:
Given: 5x – 12 = 3 (x + 2)
Prove: x = 9
Statement
Reason
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
Mrs. McConaughy
Geometry
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Example B:
If ax + b = c, then x = (c-b)/a; a ≠ 0.
Given: ax + b = c
Prove: x = (c-b)/a
Statement
Reason
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
Mrs. McConaughy
Geometry
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Final Checks For Understanding
If each statement in the first column is given
information, for the corresponding conclusion?
Given
RT + LM = 19; LM = 7
m AB = 25
AZ = 26
Mrs. McConaughy
Conclusion
RT= 12
2 (mAB) = 50
AZ/2 = 13
Geometry
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Homework Assignment #1
Writing Simple Algebraic Proofs
Supplemental WS, plus page 91-92:
1, 2 3,
Mrs. McConaughy
Geometry
10