Question

NO LINKS!! Please help me with the Segment Proofs Part 2​

Answer 1

1. Given.

2. Definition of congruent segments.

3. Segment Addition Postulate.

4. Substitution Property of Equality.

5. Transitive Property of Equality.

6. Subtraction Property of Equality.

7. Definition of congruent segments.

Explanation:

Statement 1

`\overline{AB} \cong \overline{CD}; \; \overline{CE} \cong \overline{AE}`

Reason: Given.

Statement 2

`AB=CD; \;CE=AE`

Reason: Definition of congruent segments.

Congruent segments are segments that have the same length.

Statement 3

`AE+EB=AB; \; CE+ED=CD`

Reason: Segment Addition Postulate.

A line segment divided into smaller pieces is the sum of the lengths of all those smaller segments.

Statement 4

`CE+EB=CD`

Reason: Substitution Property of Equality.

For all numbers a and b, if a=b, then a may be replaced by b in any equation or expression.

Statement 5

`CE+ED=CE+EB`

Reason: Transitive Property of Equality.

For all numbers a, b and c, if a=b and b=c, then a=c.

Statement 6

`ED=EB`

Reason: Subtraction Property of Equality.

For all numbers a, b and c, if a=b, then a-c=b-c.

Statement 7

`\overline{ED} \cong \overline{EB}`

Reason: Definition of congruent segments.

Congruent segments are segments that have the same length.