1. Proving Segment Relationships

2. Write proofs involving segment addition.
Write proofs involving segment congruence.
Standard 4.0 Students prove basic theorems involving congruence and similarity. (Key)
Lesson 7 MI/Vocab

3. Segment Addition Postulate
If B is b/t A and C, then AB + BC = AC.
If AB + BC = AC, then B is b/t A and C. 13 AC A B C 5 8 AB BC
If AB = 5 and BC = 8, then AC = = 13.

4. Segment Addition PostulateB C
AB + BC = AC
(3x + 2) + (5x – 3) = 15
8x –1 = 15
8x = 16
x = 2
If AB = 3x + 2
BC = 5x – 3
AC = 15
Solve for x.

5. Proof with Segment Addition
Prove the following.
Given: PR = QS
Prove: PQ = RS
Proof:
Statements Reasons
1. Given
PR = QS 1.
2. Subtraction Property
PR – QR = QS – QR 2.
3. Segment Addition Postulate
PR – QR = PQ; QS – QR = RS 3.
4. Substitution
PQ = RS 4.
Lesson 7 Ex1

6. Given: AC = AB AB = BX CY = XD
Prove the following.
Given: AC = AB AB = BX CY = XD
Prove: AY = BD
Lesson 7 CYP1

7. Which choice correctly completes the proof?
Statements Reasons
Which choice 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.
5. ________________
AC + CY = AY; BX + XD = BD 5. ?
Segment Addition
AY = BD
6. Substitution 6.
Lesson 7 CYP1

8. Lesson 7 TH1

9. Proof with Segment Congruence
Prove the following.
Given:
Prove:
Lesson 7 Ex2

10. Proof with Segment Congruence Given: Prove:
Statements Reasons 1.
1. Given 2.
2. Definition of congruent segments 3.
3. Given 4.
4. Transitive Property 5.
5. Symmetric Property
Lesson 7 Ex2

11. Prove the following.
Given:
Prove:
Lesson 7 CYP2

12. 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. ?
Symmetric Property
Lesson 7 CYP2

13. Homework
Chapter 2-7
Pg 121
1 – 3, 16, 19 – 29