Answer:
Part 1) [tex]BC=68\ units[/tex]
Part 2) [tex]DE=36\ units[/tex]
Part 3) [tex]CE=34\ units[/tex]
Step-by-step explanation:
we know that
The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side
so
Part 1) Find the length of BC
Applying the Midpoint Theorem
[tex]DF=\frac{1}{2}BC[/tex]
we have
[tex]DF=34\ units[/tex]
substitute the given value
[tex]34=\frac{1}{2}BC[/tex]
solve for BC
[tex]BC=34(2)=68\ units[/tex]
Part 2) Find the length of DE
Applying the Midpoint Theorem
[tex]DE=\frac{1}{2}AC[/tex]
we have
[tex]AC=72\ units[/tex]
substitute the given value
[tex]DE=\frac{1}{2}(72)[/tex]
[tex]DE=36\ units[/tex]
Part 3) Find the length of CE
we know that
[tex]BC=CE+BE[/tex] ----> by addition segment postulate
The point E is the midpoint segment BC
That means
[tex]CE=BE[/tex]
so
[tex]BC=2CE[/tex]
we have
[tex]BC=68\ units[/tex]
substitute
[tex]68=2CE[/tex]
solve for CE
[tex]CE=68/2[/tex]
[tex]CE=34\ units[/tex]
