Answered

Discover new perspectives and gain insights with IDNLearn.com's diverse answers. Our platform provides prompt, accurate answers from experts ready to assist you with any question you may have.

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

Given: [tex]A B = C D[/tex] and [tex]B C = D E[/tex]
Prove: [tex]A C = C E[/tex]

Statements | Reasons
---|---
1. [tex]A B = C D[/tex] | Given
2. [tex]B C = D E[/tex] | Given
3. [tex]A B + B C = C D + B C[/tex] | Addition Property of Equality
4. [tex]C D + B C = C D + D E[/tex] | Substitution Property of Equality (substitute [tex]B C[/tex] with [tex]D E[/tex])
5. [tex]A B + B C = A C[/tex] | Segment Addition Postulate
6. [tex]C D + D E = C E[/tex] | Segment Addition Postulate
7. [tex]A C = C E[/tex] | Substitution Property of Equality (substitute [tex]A B + B C[/tex] with [tex]A C[/tex] and [tex]C D + D E[/tex] with [tex]C E[/tex])

Type the correct answer in the box.
B [tex]I \underline{\cup} X^2 X_2 14 p t[/tex]

Sagot :

GinnyAnsweridn
Here's a detailed two-column proof for the given problem.

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

Let's break down each part of the proof:

1. Statement: [tex]\( AB = CD \)[/tex]
- Reason: Given

2. Statement: [tex]\( BC = DE \)[/tex]
- Reason: Given

3. Statement: [tex]\( AB + BC = CD + BC \)[/tex]
- Reason: Addition property of equality (we add [tex]\( BC \)[/tex] to both sides of the equalities in previous steps)

4. Statement: [tex]\( CD + BC = CD + DE \)[/tex]
- Reason: Substitution property of equality (replacing [tex]\( BC \)[/tex] with [tex]\( DE \)[/tex] based on step 2)

5. Statement: [tex]\( AB + BC = AC \)[/tex]
- Reason: Segment addition (defining [tex]\( AC \)[/tex] as the combined length of segments [tex]\( AB \)[/tex] and [tex]\( BC \)[/tex])

6. Statement: [tex]\( CD + DE = CE \)[/tex]
- Reason: Segment addition (defining [tex]\( CE \)[/tex] as the combined length of segments [tex]\( CD \)[/tex] and [tex]\( DE \)[/tex])

7. Statement: [tex]\( AC = CE \)[/tex]
- Reason: Substitution property of equality (replacing [tex]\( AB + BC \)[/tex] with [tex]\( AC \)[/tex] and [tex]\( CD + DE \)[/tex] with [tex]\( CE \)[/tex] from steps 5 and 6)
We are happy to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. Thank you for choosing IDNLearn.com. We’re committed to providing accurate answers, so visit us again soon.