1. 2. 6 Prove Statement about Segments and Angles 2
2.6 Prove Statement about Segments and Angles 2.7 Prove angle pair relationships

2. Theorem 2.1 Congruence of Segments
Segment congruence is reflexive, symmetric and transitive.
Reflexive – For any segment AB, AB AB.
Symmetric – If AB CD, then CD AB.
Transitive – If AB CD and CD EF,
then AB EF.

3. Theorem 2.2 Congruence of Angles
Angle congruence is reflexive, symmetric and transitive
Reflexive – For any angle A, A A.
Symmetric – If A B, then B A.
Transitive – If A B and B C,
then A C.

4. Example 1 Writing Two Column Proof:
Given:
Prove:
Statements Reasons 1. 2. 3. 4.
Given
Definition of congruent angles
Symmetric Property
Definition of congruent angles

5. Example 2: Given: AC = AB + AB Prove: AB = BC Statements Reasons
AB + BC = AC
AB + AB = AB + BC
AB = BC
Given
Segment Addition Postulate
Transitive Property
Subtraction Property

6. Example 3: Given: M is the midpoint of AB Prove: AB = 2AM
Statements Reasons
M is the midpoint of AB
AM = MB
AM + MB = AB
AM + AM = AB
2AM = AB
Given
Definition of midpoint
Definition of congruent segments
Segment Addition Postulate
Substitution Property
Simplify or Collect Like Terms

7. Shopping Mall Example
Walking down a hallway at the mall, you notice the music store is halfway between the food court and the shoe store. The shoe store is halfway between the music store and the bookstore. Prove that the distance between the entrances of the food court and music store is the same as the distance between the entrances of the shoe store and bookstore.

8. Shopping Mall Example STEP 1 Draw and label a diagram. STEP 2
Draw separate diagrams to show mathematical relationships.
STEP 3
State what is given and what is to be proved for the situation.
Then write a proof.

9. Shopping Mall Example Given Definition of midpoint
B is the midpoint of AC .
C is the midpoint of BD .
PROVE:
AB = CD
STATEMENT
REASONS 1.
B is the midpoint of AC .
C is the midpoint of BD . 1.
Given 2.
AB BC 2.
Definition of midpoint 3.
BC CD 3.
Definition of midpoint 4.
AB CD 4.
Transitive Property of Congruence 5.
AB = CD 5.
Definition of congruent segments

10. Theorem 2.3 Right Angles Congruence Theorem –
All right angles are congruent

11. Theorem 2.4 Congruent Supplements Theorem
If two angles are supplementary to the same angle (or to congruent angles), then they are congruent. 1 2 3
If and are supplementary and
3 and are supplementary,
then

12. Theorem 2.5 Congruent Complements Theorem
If two angles are complementary to
the same angle (or to congruent angles), then they are congruent. 4 5 6
If and are complementary and
6 and are complementary,
then

13. Extra Information Postulate 12 – Linear Pair Postulate
If two angles form a linear pair, then they are supplementary.
Theorem 2.6- Vertical Angles Congruence Theorem
Vertical Angles are congruent.

14. Example 1
Identify the pairs of congruent angles. Explain how you know they are congruent.
Answer:

15. Example 2 Answers 15. m 3 = 38o 16. m DGE = 98o 17. m CGE = 136o
19. m AGC = 142o

16. Homework Assignment Textbook Page 108-109 # 3, 4, 16 Textbook Page 113
# 3, 5, 9, 11, 17, 19