Answered

IDNLearn.com is the place where your questions are met with thoughtful and precise answers. Get the information you need from our community of experts who provide accurate and thorough answers to all your questions.

Write the following paragraph proof as a two-column proof.

Given: [tex]\(AB = CD\)[/tex] and [tex]\(BC = DE\)[/tex]
Prove: [tex]\(AC = CE\)[/tex]

| Statements | Reasons |
|---------------------------------------|-------------------------------------|
| 1. [tex]\(AB = CD\)[/tex] | 1. Given |
| 2. [tex]\(BC = DE\)[/tex] | 2. Given |
| 3. [tex]\(AB + BC = CD + BC\)[/tex] | 3. Addition Property of Equality |
| 4. [tex]\(CD + BC = CD + DE\)[/tex] | 4. Substitution Property of Equality |
| 5. [tex]\(AB + BC = CD + DE\)[/tex] | 5. Substitution Property of Equality |
| 6. [tex]\(AB + BC = AC\)[/tex] | 6. Segment Addition Postulate |
| 7. [tex]\(CD + DE = CE\)[/tex] | 7. Segment Addition Postulate |
| 8. [tex]\(AC = CE\)[/tex] | 8. Substitution Property of Equality |

Sagot :

GinnyAnsweridn
Certainly! Below is the two-column proof for the given argument:

[tex]\[ \begin{array}{|c|c|} \hline \textbf{Statements} & \textbf{Reasons} \\ \hline 1. \, AB = CD & 1. \, \text{Given} \\ \hline 2. \, BC = DE & 2. \, \text{Given} \\ \hline 3. \, AB + BC = CD + BC & 3. \, \text{Addition property of equality} \\ \hline 4. \, AB + BC = CD + DE & 4. \, \text{Substitution (using BC = DE)} \\ \hline 5. \, AB + BC = AC & 5. \, \text{Segment addition} \\ \hline 6. \, CD + DE = CE & 6. \, \text{Segment addition} \\ \hline 7. \, AC = CE & 7. \, \text{Substitution (replacing AB + BC with AC and CD + DE with CE)} \\ \hline \end{array} \][/tex]

This two-column proof corresponds to the given paragraph explanation and logically shows each step and its justification, leading to the conclusion that [tex]\( AC = CE \)[/tex].
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for visiting IDNLearn.com. We’re here to provide dependable answers, so visit us again soon.