Medians and Midsegments

ASB Math Week 3 Practice

Topics:

• Median of a Triangle

• Midsegment (Triangles + Trapezoids)

Median of a Triangle

Definition

A line segment drawn from a vertex to the midpoint of the opposite side of the vertex.

Fill in the Blank

EXAMPLE: In $$\Delta PQR$$ , $$\overline{RS}$$ is a median. If $$PQ=7$$ inches, find PS.

Fill in the Blank

YOU TRY: In $$\Delta ABC$$ , $$\overline{AD}$$ and $$\overline{CE}$$ are medians. If AE = 6 feet and BC = 14 feet, determine BE and CD.

Median of a Triangle

Centroid

• The point that all medians of a triangle intersect inside the triangle.

• Cuts a median in a ratio of 2:1.

Fill in the Blank

EXAMPLE: In $$\Delta PQR$$ , $$\overline{PS}$$ and $$\overline{QT}$$ are medians. Find TG if GQ = 17 inches.

Fill in the Blank

YOU TRY: In $$\Delta JKL$$ , $$\overline{JM}$$ and $$\overline{LN}$$ are medians. Determine LG if GN = 1 yard.

Midsegment of a Triangle

Definition

Fill in the Blank

EXAMPLE: In $$\Delta CAD$$ , $$\overline{BE}$$ is a midsegment. Find CD.

Fill in the Blank

YOU TRY: In $$\Delta PQT$$ , $$\overline{RS}$$ is a midsegment. Find PQ.

Midsegment of a Trapezoid

Definition

Fill in the Blank

EXAMPLE: In trapezoid $$PART$$ , $$\overline{MD}$$ is a midsegment. Find MD.

Fill in the Blank

YOU TRY: In trapezoid $$PART$$ , $$\overline{MD}$$ is a midsegment. Find RT.