Question

in the figure below, b is between a and c, and c is between b and d. if ac = 6, bd = 7, and ad = 9, find bc.

Explanation:

Step1: Use segment - addition postulate

We know that \(AD=AC + CD\). Given \(AD = 9\) and \(AC=6\), we can find \(CD\).
\[CD=AD - AC\]
\[CD=9 - 6=3\]

Step2: Use segment - addition postulate again

We know that \(BD=BC + CD\). Given \(BD = 7\) and \(CD = 3\), we can find \(BC\).
\[BC=BD - CD\]
\[BC=7 - 3 = 4\]

Answer:

4