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.

$\overline{MT}$bisects $\overline{LH}$.

Short answer

The statement $\overline{MT}$bisects$\overline{LH}$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 $\overline{LM}=\overline{MH}$.

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 $\overline{HL}$.

This implies that $\overleftrightarrow{KT}$bisects $\overline{LH}$and $\overline{MT}$is also a part of $\overleftrightarrow{KT}$and its one endpoint is the mid-point of $\overline{LH}$, so it is true that $\overline{MT}$bisect $\overline{LH}$.

Therefore, the statement$\overline{MT}$ bisect $\overline{LH}$is true.