Question

In the following diagram $\overline{HL}$and $\overleftrightarrow{KT}$intersect at the midpoint of $\overline{HL}$. Classify the following statement as true or false.

$\overline{LM}\cong \overline{MH}$

Short answer

The statement$\overline{LM}\cong \overline{MH}$ is true.

Step-by-step solution

Step 1. Check the figure.

Consider the figure.

Step 2. Apply the concept of midpoint.

A midpoint is a point lying between two points and is in the middle of the line joining the two points.

Here 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$\overline{MH}$such that $\overline{LM}\cong \overline{MH}$.

Step 3. Step description.

As$\overline{HL}$ and$\overleftrightarrow{KT}$ intersect at the midpoint of$\overline{HL}$ and that intersection point is $M$, thus$M$is the midpoint of $\overline{HL}$.

Therefore, the statement $\overline{LM}\cong \overline{MH}$is true.