Proving Segment Relationships Write proofs involving segment addition

Proving Segment Relationships

• Write proofs involving segment addition. • Write proofs involving segment congruence. Standard 4. 0 Students prove basic theorems involving congruence and similarity. (Key)

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. A B AB 5 AC 13 C BC 8 If AB = 5 and BC = 8, then AC = 5 + 8 = 13.

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

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

Prove the following. Given: AC = AB AB = BX CY = XD Prove: AY = BD

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

Proof with Segment Congruence Prove the following. Given: Prove:

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

Prove the following. Given: Prove:

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

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