Question

given: c is the mid - point of bd prove: ab + cd = ac statements reasons 1. c is the mid - point of bd 1. given 2. definition of a midpoint 3. segment addition postulate 4. ab + cd = ac

Explanation:

Step1: Apply mid - point definition

Since C is the mid - point of $\overline{BD}$, then $BC = CD$.

Step2: Apply segment addition postulate

By the segment addition postulate, $AB+BC = AC$.

Step3: Substitute

Substitute $BC$ with $CD$ (from step 1) into the equation $AB + BC=AC$. We get $AB + CD=AC$.

Answer:

The proof is completed as above. The missing statements and reasons are filled as follows:

1. $BC = CD$; Definition of a Midpoint
2. $AB+BC = AC$; Segment Addition Postulate
3. Substitution (substituting $BC$ with $CD$)