Q9. - 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.

 

$\overrightarrow{MT}$ and $\overrightarrow{TM}$ are opposite rays.

Step-by-Step Solution

Answer

The statement “$\overrightarrow{MT}$ and $\overrightarrow{TM}$ are opposite rays” is false.

Step 1. Check the figure.

Consider the figure.

Step 2. Apply the concept of opposite rays.

Opposite rays are those rays that start from a common point but goes in the opposite directions. 

Step 3. Step description.

Here $\overrightarrow{MT}$ and $\overrightarrow{TM}$ both are in opposite directions but both the rays do not have a common starting point. Thus, they are not opposite rays.

 

Therefore, the statement “$\overrightarrow{MT}$ and $\overrightarrow{TM}$ are opposite rays” is false.