Q7. - Geometry

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 $\overline{LH}$.

 

Step-by-Step Solution

Answer

The statement $\overline{MT}$ bisects $\overline{LH}$ is true.

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.