Question

Given: D is the midpoint of CE prove : DR = 1/2CE Reason bank simply Transitive property Division property Addition property Given Definition of midpoint Segment Addition postulate

Answer 1

SOLUTION

Statement1: Given a line segment

$CE$

Statement 2: Definition of Midpoint

D as the midpoint

Then we have

Statement 3: Segment addition postulate

$\begin{gathered} CD+DE=CE \\ \text{ } \end{gathered}$

Statement 4: simplify

$CE=DE$

Statement 5: Addition property

Then Adding DE to both sides

$\begin{gathered} CD+DE=DE+DE \\ CD+DE=2DE \end{gathered}$

Then from the diagram,

$CD+DE=CE$

We have

Statement 6: Transitive property

$\begin{gathered} CE=CD+DE=2DE \\ \text{then } \\ CE=2DE \end{gathered}$

statement 7: Division property

Divide both sides by 2

$\begin{gathered} \frac{CE}{2}=\frac{2DE}{2} \\ \\ DE=\frac{1}{2}CE \end{gathered}$

Therefore

DE=1/2 CE implies D is the midpoint of CE

Statement 1= Given

Statement2=Difine a midpoint

Statement 3=Segment addition postulate

statement 4=simplify

Statement5= Addition property

Statement 6=transitive property

Statement 7=Division property