Consider the statement for your answers in numbers 11 and 12. Given: A,, C,and D are collinear in that order and AB = CD. Prove: AC = BD Statements Reasons 1. A, B, C,and D are collinear, in Given that order. 2. AB = CD Given 3. BC = BC (11) 4. AB + BC = BC + CD Addition Property of Equality 5. AB + BC = AC (12) BC+CD= BD 6. AC = BD Substitution Property 11. What is the "reason" for step 3 of the proof? A. Commutative Property B. Reflexive Property C. Symmetric Property 12. What is the "reason" for step 5 of the proof? A. Angle Addition Postulate C. Commutative Property of Equality D. Distributive Property of Equality B. Segment Addition Postulate For the statement in numbers 13, 14, and 15. Consider the points A, B, and C are collinear. Prove: If AB=AC, then B is the midpoint of AC. Statements Reasons D. Transitive Proper
Consider the statement for your answers in numbers 11 and 12. Given: A,, C,and D are collinear in that order and AB = CD. Prove: AC = BD Statements Reasons 1. A, B, C,and D are collinear, in Given that order. 2. AB = CD Given 3. BC = BC (11) 4. AB + BC = BC + CD Addition Property of Equality 5. AB + BC = AC (12) BC+CD= BD 6. AC = BD Substitution Property 11. What is the "reason" for step 3 of the proof? A. Commutative Property B. Reflexive Property C. Symmetric Property 12. What is the "reason" for step 5 of the proof? A. Angle Addition Postulate C. Commutative Property of Equality D. Distributive Property of Equality B. Segment Addition Postulate For the statement in numbers 13, 14, and 15. Consider the points A, B, and C are collinear. Prove: If AB=AC, then B is the midpoint of AC. Statements Reasons D. Transitive Proper
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider the statement for your answers in numbers 11 and 12.
Given: A, C,and D are collinear in that order and AB = CD. Prove: AC = BD
Statements
1. A, B,C,and D are collinear, in Given
Reasons
that order.
2. AB = CD
3. BC = BC
4. AB + BC = BC + CD
Given
(11)
Addition Property of Equality
5. AB + BC = AC
(12)
BC + CD = BD
6. AC = BD
Substitution Property
11. What is the "reason" for step 3 of the proof?
A. Commutative Property
C. Symmetric Property
B. Reflexive Property
D. Transitive Propet
12. What is the "reason" for step 5 of the proof?
A. Angle Addition Postulate
B. Segment Adition Postulate
C. Commutative Property of Equality
D. Distributive Property of Equality
For the statement in numbers 13, 14, and 15.
Consider the points A, B, and C are collinear.
Prove: If AB =- AC, then B is the midpoint of AC.
Statements
Reasons
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