Q16. - 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.

$TM+MH=TH$

Step-by-Step Solution

Answer

The statement “$TM+MH=TH$” is false.

Step 1. Check the figure.

Consider the figure.

Step 2. Step description.

Here, $\overline{HL}$ and $\overleftrightarrow{KT}$ intersect at the midpoint of $\overline{HL}$ and the midpoint is $M$.

Step 3. Step description.

Since $M$ is not the midpoint of $TH$, thus the length of $TM+MH$ is not equal to $TH$.

 

Therefore, the statement is false.

 

Therefore, the statement “$TM+MH=TH$” is false.