1. To complete proofs involving angle theorems
Geometry Proofs
Obj: To Complete Proofs Involving Segment Theorems
To complete proofs involving angle theorems

2. 5 Essential Parts to a Good Proof
State the theorem to be proved
List the given information
If possible draw a diagram to illustrate the given information
State what is to be proved
Develop a system of deductive reasoning

3. Deductive Reasoning
Definitions & postulates-Statements accepted as true w/o proof
Theorem- undefined terms that can be used as truth once they have been proven

4. Theorem:
Congruence of segments is reflexive, symmetric, and transitive
Written as symbols:
Reflexive:
Symmetric: IF
, then
Transitive: IF
and
then

5. Example: 1.) _________ 2.) AD = AB + BD 2.) ___________C D
Given:
Prove:
Statements
Justification
1.) _________
Given
2.) AD = AB + BD
2.) ___________
Seg. + post
Seg. + post.
3.) BD = BC + CD
3.)___________
4.) AD = AB + BC + CD
4.)___________
substitution

6. Your Turn: Given: pts PQRS are collinear Prove: PQ = PS - QS P Q R S
Statement
Justification
1.) pts PQRS are collinear
2.) PS = PQ + QS
3.) PS – QS = PQ
4.) PQ = PS - QS

7. Solution to “Your Turn”:P Q R S
Given: pts PQRS are collinear
Prove: PQ = PS - QS
Statement
Justification
1.) pts PQRS are collinear
1.) Given
2.) PS = PQ + QS
2.) Seg. + post
3.) PS – QS = PQ
3.) Subtraction
4.) PQ = PS - QS
4.) symmetric Prop.

8. Verifying Angle Relationships

9. Theorems
Supplement thm-if 2 angles form a linear pr then they are supplementary
Congruence of angles is reflexive, symmetric, and transitive
Angles supplementary to the same angle or to congruent angles are congruent

10. Theorems Continued
Angles complementary to the same angle or congruent angles are congruent
All right angles are congruent
Vertical angles are congruent
Perpendicular lines intersect to form 4 right angles

11. Example: If and are vertical , and . Find
Angle A = Angle C, Vert. angles
3x - 2 = 2x + 4
A = 3(6) - 2
-2x x +2
= 16o
x = 6
C = 2 (6) + 4
= 16o

12. Your Turn: Find the measure of each numbered angle 1 2
2x x - 4 = 180
2 (63) - 5 = 121o
= 59o
3x - 9 = 180
3x = 189
x = 63

13. Homework: Put this in your agenda: Pg 116 5 – 12, 21 – 24
Pg – 21 odd,