1. BELL RINGER PROBLEM
State the property that justifies the statement. If BC = CD and CD = EF, then BC = EF.
A. Reflexive Property
B. Symmetric Property
C. Substitution Property
D. Transitive Property
You do not necessarily need to put this in your notes, but be prepared to give your answer and your reasoning behind why you chose your answer.
5-Minute Check 5

2. You wrote algebraic and two-column proofs.
Write proofs involving segment addition.
Write proofs involving segment congruence.
Then/Now

3. Concept

4. Concept

5. Concept

6. Concept

7. Concept

8. Reflexive Property of Equality Substitution Property of Equality
Use the Segment Addition Postulate
You will use each of the following (not necessarily in this order):
Given
Reflexive Property of Equality
Substitution Property of Equality
Transitive Property of Equality
Definition of Congruent Segments (used twice)
Segment Addition Postulate (used twice)
Example 1

9. 2. Definition of congruent segments AB = CD 2.
Use the Segment Addition Postulate
Proof:
Statements Reasons 1.
1. Given
AB  CD
___
2. Definition of congruent segments
AB = CD 2.
3. Reflexive Property of Equality
BC = BC 3.
4. Segment Addition Postulate
AB + BC = AC 4.
Example 1

10. 5. Substitution Property of Equality 5. CD + BC = AC
Use the Segment Addition Postulate
Proof:
Statements Reasons
5. Substitution Property of Equality
5. CD + BC = AC
6. Segment Addition Postulate
CD + BC = BD 6.
7. Transitive Property of Equality
AC = BD 7.
8. Definition of congruent segments 8.
AC  BD
___
Example 1

11. Which reason correctly completes the proof?
1. Given
AC = AB, AB = BX 1.
2. Transitive Property
AC = BX 2.
3. Given
CY = XD 3.
4. Addition Property
AC + CY = BX + XD 4.
AY = BD
6. Substitution 6.
Proof:
Statements Reasons
Which reason correctly completes the proof?
5. ________________
AC + CY = AY; BX + XD = BD 5. ?
Example 1

12. C. Definition of congruent segments
A. Addition Property
B. Substitution
C. Definition of congruent segments
D. Segment Addition Postulate
Example 1

13. Proof Using Segment Congruence
BADGE Jamie is designing a badge for her club. The length of the top edge of the badge is equal to the length of the left edge of the badge. The top edge of the badge is congruent to the right edge of the badge, and the right edge of the badge is congruent to the bottom edge of the badge. Prove that the bottom edge of the badge is congruent to the left edge of the badge.
Given:
Prove:
Example 2

14. 2. Definition of congruent segments 2.
Proof Using Segment Congruence
Proof:
Statements Reasons
1. Given 1.
2. Definition of congruent segments 2.
3. Given 3.
4. Transitive Property 4. YZ
___
5. Substitution 5.
Example 2

15. Prove the following.
Given:
Prove:
Example 2

16. Which choice correctly completes the proof? Proof:
Statements Reasons
1. Given 1.
2. Transitive Property 2.
3. Given 3.
4. Transitive Property 4.
5. _______________ 5. ?
Example 2

17. C. Segment Addition Postulate
A. Substitution
B. Symmetric Property
C. Segment Addition Postulate
D. Reflexive Property
Example 2

18. Remember: You have a QUIZ on Friday over 2-6 & 2-7
HW: (2-7) Worksheet
Remember: You have a QUIZ on Friday over 2-6 & 2-7
Concept