1. Proving Angles Congruent
An Introduction to Geometric Proofs

2. Proof
Is a set of deductive steps which are used to show that a conditional statement (or “Theorem”) is true. Each step is justified by a
)postulate,
) property,
)definition,
)algebraic rules (“Simplify”),
) previously proved theorem or
)as “Given” information

3. In a Paragraph Proof…
Each step and reason is written as a sentence in a paragraph.
“Given” info is explicitly stated or shown in a diagram
* “Prove” the conclusion of the conditional; it is the last part of the proof.

4. Sample Paragraph Proofs
Ex. 3 page 98: Vertical angles are congruent.

5. Congruent Supplements Theorem
If 2 angles are supplements of the same angle (or of congruent angles), then the two angles are congruent.

6. Congruent Complements Theorem
If 2 angles are complements of the same angle (or of congruent angles), then the two angles are congruent.
Draw a picture…..
Given:
Prove:

7. Paragraph Proof By definition of congruence,
By definition of complementary angles,
_____________________________
By substitution (or transitive p of =),
____________________________
By subtraction p of =, ___________
By definition of congruence,
q.e.d.! (quod est demonstratum)

8. All Right Angles are Congruent
Draw a picture…
Given…..
Prove…..

9. Paragraph Proof By definition of right angles,
_________________________
By substitution (or transitive p of =),
____________________________
By definition of congruence, ________________________
q.e.d.! (quod est demonstratum)

10. If two angles are congruent and supplementary, then each is a right angle.
Draw a picture…
Given…..
Prove…..

11. Paragraph Proof By definition of congruent angles,
__________________________
By definition of supplementary angles,____________________
Substituting one angle measure for the other yields______________
Which then simplifies into ________.
Use the division p of = to get____________.
Because the angles are congruent, ________________ and by the definition of right angles, both angles must be_____________
q.e.d!