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Q6

Expert-verified
Found in: Page 15

### Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279

# In the following diagram $\overline{)HL}$ and role="math" localid="1637753977355" $\stackrel{↔}{KT}$ intersect at the midpoint of $\overline{)HL}$. Classify the following statement as true or false. KM must equal to MT.

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

See the step by step solution

## 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 role="math" localid="1637754449037" $\overline{)LM}$ is equal to the length of the line segment role="math" localid="1637754557956" $\overline{)MH}$ such that $\overline{)LM}=\overline{)MH}$.

## Step 3. Step description.

As $\overline{)HL}$ and $\stackrel{↔}{KT}$ 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.