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Proofs
2.5/2.6 Notes
Using Proof In Algebra and Geometry and 2 column proofs
Properties of Equality for Real Numbers
Reflexive
Symmetric
Transitive
Addition and Subtraction
Multiplication and Division
Substitution
Distributive
Now let’s look at how these properties from algebra can be used to discuss relationships between
segments measures and also angle measures…
Property
Segments
Angles
Theorem
Linear pair theorem
If 2 angles form a linear pair, then they are
supplementary
Hypothesis
Conclusion
Congruent Supplements Theorem
If 2 angles are supplementary to the same angle (or
to 2 congruent angles), then the 2 angles are
congruent.
Right Angle congruence
All right angles are congruent.
Congruent Complements Theorem
If 2 angles are complementary to the same angle
(or to 2 congruent angles), then the 2 angles are
congruent.
Example 1: Name the property of equality that justifies each statement
Statements
a.
If AB + BC = DE, then AB = DE
b.
c. If XY = PQ and XY = RS, then PQ = RS
d. If
e. If
Reasons
Example 2: Prove If (3x + 5)/2 = 7, then x = 3
Statements
Reasons
1.
The types of proofs we just constructed are called _______________________________________ OR
__________________________________________ .
Example 3: Justify the steps for the proof of
If PR = QS, then PQ = RS
Given: __________
Prove: ___________
Statements
Reasons
1. PQ = QS
2. PQ + QR = PR
QR + RS = QS
3. PQ +QR = QR +RS
4. PQ = RS
1 _____________________
2 _____________________
3 ____________________
4 ____________________
Example 4: Justify the steps for the proof of:
If
Statements
Reasons
1)
1) Given
2) mABD  mDBC  90
2)
3)
3) Angle addition postulate
4)
5)
mABC  90
4)
5) Definition of a right
angle
The Proof Process (p.112) Write the steps here. It will help you in the future I
promise! 