Question

determine the correct responses to complete each row of the proof. *
complete the two - column proof.
given: $overline{ab}congoverline{cd}$
prove: $overline{ac}congoverline{bd}$

1. $overline{ab}congoverline{cd}$ given
2. reflexive property

3.

1. $ab + bc=ac$ $cd + bc=bd$
2. $cd + bc=ac$ substitution property
3. substitution property
4. $overline{ac}congoverline{bd}$

Explanation:

Step1: Identify reflexive property statement

$BC\cong BC$

Step2: State segment - addition postulate reason

Segment - Addition Postulate

Step3: Identify substitution for final proof

$AC = BD$ (since $CD + BC=AC$ and $CD + BC = BD$), then by the definition of congruent segments (if two segments have the same length, they are congruent), we have $\overline{AC}\cong\overline{BD}$

Answer:

Statement	Reason
2. $\overline{BC}\cong\overline{BC}$	Reflexive Property
3.	Segment - Addition Postulate
4. $AB + BC=AC$, $CD + BC = BD$	Segment - Addition Postulate
5. $CD + BC=AC$	Substitution Property
6. $AC = BD$	Substitution Property
7. $\overline{AC}\cong\overline{BD}$	Definition of congruent segments