Page 198 - Math Course 2 (Book 2)

Proving Segment Relationships

Proof with Segment Congruence Proof with Segment Congruence
Which choice correctly completes the proof?
Example A

B
Prove the following.
Given: WY = YZ Y 3 cm Z C E
YZ ≅ XZ
XZ ≅ WX 3 cm Prove the following. G
Prove: WX ≅ WY Given: GD ≅ BC
Proof: W X BC ≅ FH D
Statements Reasons FH ≅ AE
1. WY = YZ 1. Given Prove: AE ≅ GD F
2. Definition of congruent Proof:
2. WY ≅ YZ H
segments Statements Reasons
3. YZ ≅ XZ; XZ ≅ WX 3. Given 1. GD ≅ BC, BC ≅ FH 1. Given
4. WY ≅ WX 4. Transitive Property 2. GD ≅ FH 2. Transitive Property
5. WX ≅ WY 5. Symmetric Property 3. FH ≅ AF 3. Given
4. GD ≅ AE 4. Transitive Property
Your Turn! 5. AE ≅ GD 5. _______________

A. Substitution
Proof with Segment Addition B. Symmetric Property
A B C. Segment Addition Postulate
Prove the following. D. Reflexive Property
Given: AC = AB
AB = BX
CY = XD C X Answer
Prove: AY = BD Y D
Proof:
Statements Reasons E
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; 5. _______________
BX + XD = BD
6. AY = BD 6. Substitution

A. Addition Property
B. Substitution
C. Definition of congruent symbols
D. Segment Addition Postulate

Answer

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