Q6 - 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. 

KM must equal to MT.

Step-by-Step Solution

Answer

The statement “KM  must equal to MT ” is false.

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 $\overline{LM}\cong \overline{MH}$ 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 $\overline{HL}$ but this does not imply that $KM$ must equal to $MT$.

 

Therefore, the statement “KM must equal to MT ” is false.