Chapter 1.3, Problem 5WE

To determine

To verify: if the given statement is true or false.

  $\overline{LM}\cong \overline{MH}$

Answer to Problem 5WE

True

Explanation of Solution

Given:

In the figure below $\overline{HL}$ and $\overleftrightarrow{KT}$ intersect at the midpoint of $\overline{HL}$ .

The statement $\overline{LM}\cong \overline{MH}$ implies that the length of the line segment $\overline{LM}$ is equal to the length of the line segment $\overline{MH}$ .

That is,

  $LM=MH$

Now the above statement is true, as it is given that $\overline{HL}$ and $\overleftrightarrow{KT}$ intersects at the midpoint of $\overline{HL}$ and that intersection point is M . That is M is the mid-point of $\overline{HL}$ .

So, the given statement is true.