Question

explain how and show examples of how to find midsegments of triangles

Answer 1

Answer on Question #43099, Math, Geometry

Task: explain how and show examples of how to find midsegments of triangles

Answer:

A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle.

In the figure $D$ is the midpoint of $\overline{AB}$ and $E$ is the midpoint of $\overline{AC}$.

So, $\overline{DB}$ is a midsegment.

A midsegment connecting two sides of a triangle is parallel to the third side and is half as long.

If $AD = DB$ and $AE = EC$, then $\overline{DB} \parallel \overline{BC}$ and $DE = \frac{1}{2} BC$.

Example:

Find the value of $x$.

Here $P$ is the midpoint of $AB$, and $Q$ is the midpoint of $BC$. So, $\overline{PQ}$ is a midsegment.

Therefore by the Triangle Midsegment Theorem, $PQ = \frac{1}{2} BC$.

$$\begin{array}{l} x = \frac{1}{2} \cdot 6 \\ = 3 \quad \text{. The value of } x \text{ is } 3. \end{array}$$

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