Q11. - 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. 

 

$\overleftrightarrow{LH}$ is same as $\overline{HL}$

Step-by-Step Solution

Answer

The statement “$\overrightarrow{LH}$ is same as $\overline{HL}$” is false.

Step 1. Check the figure.

Consider the figure.

Step 2. Apply the concept of segment and line.

A segment is a part of the line that is bounded by two endpoints. Thus, a segment has 2 endpoints.

 

A line goes on infinitely in both the direction. A line has no endpoints.

Step 3. Step description.

Here $\overline{HL}$ represents a segment. Thus $\overline{HL}$ have two endpoints $H$ and $L$ and all the points between these two points and $\overleftrightarrow{LH}$  represent a line and it is extended infinitely on both sides.

 

Since $\overline{HL}$ is a part of $\overleftrightarrow{LH}$ thus, they are not the same.

 

Therefore, the statement “$\overleftrightarrow{LH}$  is same as $\overline{HL}$” is false.