Chapter 2.3, Problem 15WE

a.

To determine

To find: congruent segments

Answer to Problem 15WE

  $\overline{LM,}\overline{MK}$ and $\overline{GN,}\overline{NH}$

Explanation of Solution

Given information: M and N are midpoints of $\overline{LK}$ and $\overline{GH}$ respectively.

  

A midpoint is a point on a line segment that divides it into congruent segments.

As M is a midpoint of $\overline{LK}$ ,

  $\overline{LM}\cong \overline{MK}$

As N is a midpoint of $\overline{GH}$ ,

  $\overline{HN}\cong \overline{GN}$

So,

Congruent segments are $\overline{LM,}\overline{MK}$ and $\overline{GN,}\overline{NH}$

b.

To determine

To find: additional information that enables to deduce that $LM=NH$

Answer to Problem 15WE

Additional information required is $MK=GN$

Explanation of Solution

Given information: $LM=NH$

  

Use the pair of congruent segments obtained in part a.

If two segments are congruent then their measures are also equal.

From part a., $\overline{LM}\cong \overline{MK}$

So,

  $LM=MK$ (i)

From part a., $\overline{HN}\cong \overline{GN}$

So,

  $HN=GN$ (ii)

Now assume that $MK=GN$ (iii)

From (i), (ii) and (iii),

  $LM=HN$

So, we get that $LM=HN$ using the assumption that $MK=GN$