Question

problem 24
clear
given: (\triangle abc),
d is the midpoint
of (overline{ab}) and
e is the midpoint
of (overline{ac}).
prove: (overline{de}paralleloverline{bc}) and
(de=\frac{1}{2}bc).

1. draw (overleftrightarrow{de})
2. two points determine

a line.

1. choose point f on (overleftrightarrow{de})

so that (ef = de).

1. ruler postulate
2. draw (overline{cf}).
3. two points determine

a line.

1. (\triangle abc), e is the mid-

point of (overline{ac}).

1. given
2. (ae = ec)

5.

Explanation:

Step1: Definition of mid - point

Since \(E\) is the mid - point of \(\overline{AC}\), by the definition of a mid - point (a mid - point of a line segment divides the segment into two equal parts), we have \(AE = EC\).

Answer:

1. Definition of mid - point.