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Q6

Expert-verifiedFound in: Page 15

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" $\overleftrightarrow{KT}$ 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.**

Consider the figure.

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 $\overline{)LM}=\overline{)MH}$.

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.

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