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.

$\overleftrightarrow{KT}$is a bisector of $\overline{LH}$.

Short answer

The statement “$\overleftrightarrow{KT}$ is a bisector of $\overline{LH}$” 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 $\overline{HL}$.

Since$M$is the midpoint thus this implies that$\overleftrightarrow{KT}$ bisects $\overline{LH}$.

Therefore, the statement $\overleftrightarrow{KT}$bisects$\overline{LH}$ is true.