ANSWER and EXPLANATION
We want to find the length of each of the segments and state whether they are congruent.
To do this, find the difference between the endpoints of the segments and compare. if the two line segments have the same length then, they are congruent.
1. BD and CE
Let us find their lengths:
[tex]\begin{gathered} BD=D-B=3-(-6)=3+6=9 \\ \\ CE=E-C=7-1=6 \end{gathered}[/tex]Since the two line segments do not have the same length, they are not congruent.
2. BC and CE
Let us find their lengths:
[tex]\begin{gathered} BC=C-B=1-(-6)=1+6=7 \\ \\ CE=E-C=7-1=6 \end{gathered}[/tex]Since the two line segments do not have the same length, they are not congruent.
3. AC and BD
Let us find their lengths:
[tex]\begin{gathered} AC=C-A=1-(-8)=1+8=9 \\ \\ BD=D-B=3-(-6)=3+6=9 \end{gathered}[/tex]Since the two line segments have the same length, they are congruent.
4. AD and BE
[tex]\begin{gathered} AD=D-A=3-(-8)=3+8=11 \\ \\ BE=E-B=7-(-6)=7+6=13 \end{gathered}[/tex]Since the two line segments do not have the same length, they are not congruent.
