Question

1. $cd + db=cb$ 5. segment addition postulate
2. 6. substitution property of equality
3. $overline{ad}congoverline{cb}$ 7. definition of congruence

what is the statement for step 6?
○ $ac + cd=cd + db$
○ $cd = cd$
○ $ad = cb$
○ $overline{ad}congoverline{cb}$

Explanation:

Step1: Recall substitution property

The substitution property of equality allows us to replace one quantity with another that is equal to it. In step 5 we have $CD + DB=CB$. To get to step 7 where we have $\overline{AD}\cong\overline{CB}$ (which is based on the definition of congruence for lengths $AD = CB$), we need to substitute to get the equality of the lengths of the segments.

Step2: Analyze options

• Option 1: $AC + CD=CD + DB$ doesn't help in getting to $AD = CB$.
• Option 2: $CD = CD$ is the reflexive property and not relevant for this substitution.
• Option 3: If we assume some previous steps have led to a situation where we can substitute to get the lengths of the segments equal, and since step 7 is about congruence based on equality of lengths, the statement $AD = CB$ is a valid substitution step to get from the segment - addition related step 5 to the congruence step 7.
• Option 4: $\overline{AD}\cong\overline{CB}$ is the statement in step 7, not step 6.

Answer:

$AD = CB$