Download Unit 2.2 Proofs 3.2 NOTES NAME_______________________

Unit 2.2
Proofs
NAME_______________________ PERIOD___
Standard:
BellWork
CO.9
Find the perimeter and area of the figures below.
1.
2.
Objective:
To complete
two column
proofs.
3.2 NOTES
3.
Proofs In mathematics, a _PROOF__ is a logical argument that uses a _HYPOTHESIS_
to prove a conjecture. Once the conjecture is proved, it is called a theorem.
Each STATEMENT in a proof must follow _FACTS from what has come before
and must have a _REASON_ to support it.
The table states some properties of equality that you seen in Algebra.
PROPERTY
EXAMPLE
ADDITION PROPERTY
Properties
SUBTRACTION PRPOERTY
of Equality MULTIPLICATION PROPERTY
DIVISION PROPERTY
INVERSE PROPERTY
TRANSITIVE PROPERTY
SYMMETRIC PROPERTY
REFLEXIVE PROPERTY
The same algebraic properties of equality can apply to geometry with
segments and angles.
Congruence
Segments
and Angles
Congruent line segments: _____________ Congruent angles: _____________
Properties
of
Congruence
Congruence of Segments
Congruence of Angles
Example 1 Identify the property that justifies the property.
a. Y  Y (STATEMENT)
REASON?___________________
b. If ST  UV and UV  WX, then ST  WX (STATEMENT)
c. If FG  JK, then JK  FG (STATEMENT)
REASON?________
REASON?___________________
Checkpoint Identify the property that justifies the property.
a. IF E  I and I  O, then E  O (STATEMENT)
b. IF ABC  DEF, then DEF  ABC (STATEMENT)
c. BC  BC (STATEMENT)
REASON?_________
REASON?___________
REASON?___________________
Example 2
Given:
Statements
1. ____ + ____ = ____
Reasons
1.
Checkpoint
Given:
Statements
1. ____ and ____ are
supplementary angles
2. ____ + ____ = ____°
Reasons
1.
2.
Example 3 W, X, Y, and Z are collinear as shown in the figure.
2 COLUMN
PROOFS
Given: X is the midpoint of WY, Y is the midpoint of XZ
Prove: WX = YZ
Statements
1. X is the midpoint of WY,
Y is the midpoint of XZ
2. WX = XY and XY = YZ
3. XY = XY
4. WX = YZ
Checkpoint
Reasons
1.
2.
3.
4.
Given:
Prove: AB = 17
Statements
1. ____ + ____ = ____
2. AB + 18 = 35
3. AB = 17
Reasons
1.
2.
3.
Example 4
Given:
Prove: mVXW = mZXY
Statements
1. VXW and ZXY are formed by
intersecting lines
2. VXW and ZXY are vertical angles
3. VXW and WXZ are a linear pair;
WXZ and ZXY are a linear pair
4. VXW and WXZ are supplementary
5. VXW + WXZ = 180°
6. WXZ and ZXY are supplementary
7. WXZ + ZXY = 180°
8. mVXW + mWXZ = mWXZ + mZXY
9. mVXW = mZXY
Reasons
1.
2.
3.
4.
5.
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8.
9.