5.3 Notes Medians, Centroids, and Altitudes of Triangle

Use the Centroid Theorem to find segment lengths

median of a triangle -

centroid of a triangle-

The centroid of a triangle is located _____________________________________ from each vertex to

the midpoint of the opposite side.

Example 1 Using the Centroid to Find Segment Lengths

In Δ ABC, AF = 9, and GE = 2.4. Find each length.

a) AG

b) CE

Now you try…

In Δ JKL, ZW = 7, and LX =8.1.

Find KW and LZ.

Altitudes

Draw an altitude of the triangle. Definition of an Altitude:

Partner Practice!

Use the diagram shown and the given information to decide in each case whether EG is a

perpendicular bisector, an angle bisector, a median, or an altitude of DEF .

3. DG FG

4. EG DF

5. DEG FEG

6. EG DF and DG FG

7. DGE FGE

8. Is the median to the base of an isosceles triangle also an altitude? Explain your reasoning.

A

B

D

C