Chapter 1.6, Problem 4PSA

To determine

To Prove: $\overline{AB}\cong \overline{BC}$

Explanation of Solution

Given:

  

  $\begin{array}{l}AB=x+4\\ BC=2x\\ AC=16\end{array}$

Formula Used:

  $AC=AB+BC$

Proof:

Here, we have

  $\begin{array}{l}AB=x+4\\ BC=2x\\ AC=16\\ \because AC=AB+BC\\ \Rightarrow 16=x+4+2x\\ \Rightarrow 12=3x\\ \Rightarrow x=4\\ \therefore AB=4+4=8\\ BC=2\times 4=8\\ \Rightarrow \overline{AB}\cong \overline{BC}\end{array}$