Bell Ringer 11-8 (in your notes)You may use your notes on 2-7 only.

1. What is the title of Lesson 2-7?

2. What is the difference between a postulate and a theorem?

3. Explain the Segment Addition Postulate.

4. What are the Three Properties of Segment Congruence?

When you are finished, open your book to Lesson 2-7 and take out your notebook if you haven’t already.

Content Standards

G.CO.9 Prove theorems about lines and angles.

G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).

Mathematical Practices

2 Reason abstractly and quantitatively.

3 Construct viable arguments and critique the reasoning of others.

• Write proofs involving segment addition.

• Write proofs involving segment congruence.

Use the Segment Addition Postulate

2. Definition of congruent segments

AB = CD2.

3. Reflexive Property of EqualityBC = BC3.

4. Segment Addition PostulateAB + BC = AC4.

Proof:Statements Reasons

1. 1. GivenAB CD___ ___

6. Segment Addition PostulateCD + BC = BD6.

7. Transitive Property of EqualityAC = BD7.

Proof:Statements Reasons

5. Substitution Property of Equality

5. CD + BC = AC

Use the Segment Addition Postulate

8. Definition of congruent segments

8. AC BD___ ___

Prove the following.

Given: AC = ABAB = BXCY = XD

Prove: AY = BD

Write the given and prove statement

above, and then draw the figure.

1. GivenAC = AB, AB = BX1.

2. Transitive PropertyAC = BX2.

3. GivenCY = XD3.

4. Addition PropertyAC + CY = BX + XD4.

AY = BD 6. Substitution6.

Proof:Statements Reasons

Which reason correctly completes the proof?

5. ________________AC + CY = AY; BX + XD = BD

5. ?

A. Addition Property

B. Substitution

C. Definition of congruent segments

D. Segment Addition Postulate

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:

Proof Using Segment Congruence

5. Substitution5.

Proof:Statements Reasons

1. Given1.

2. Definition of congruent segments

2.

3. Given3.

4. Transitive Property4. YZ___

Prove the following.

Given:

Prove:

Which choice correctly completes the proof?

Proof:

Statements Reasons

1. Given1.

2. Transitive Property2.

3. Given3.

4. Transitive Property4.

5. _______________5. ?

A. Substitution

B. Symmetric Property

C. Segment Addition Postulate

D. Reflexive Property

• Class Assignment

• p. 147 1, 4