Geometry

Section 5.4 – Medians and Altitudes

Primary Vocabulary Terms in Ch. 5(Review)

1. Midsegmenta. Connects two midpointsb. Midsegment parallel to third side and half length of third side

2. Perpendicular Bisectora. Perpendicular to segment and goes through midpoint of

segmentb. All points on it are equidistant from endpoints of segment

3. Angle Bisectora. Cuts angle into two congruent piecesb. All points on it are equidistant from sides of angle

• Distance from point to side must be perpendicular to the side

Primary Vocabulary Terms in Ch. 5(New)

4. Median (Section 5.4)a. Connects vertex to

opposite midpointb. If all three medians are

drawn, they are concurrent and meet at a point called the centroid

Primary Vocabulary Terms in Ch. 5(New)

4. Median (Section 5.4)a. Connects vertex to

opposite midpointb. If all three medians

are drawn, they are concurrent and meet at a point called the centroid

c. The centroid is the center of mass of a triangle

Primary Vocabulary Terms in Ch. 5(New)

4. Median (Section 5.4)d. Theorem 5.8 – Median

Concurrency:The medians of a triangle intersect at a point that is two thirds of the distance from each vertex to the midpoint of the opposite side

e. The distance from the centroid to the midpoint is half the distance from the centroid to the vertex

Practice Problems

MP, KW, and RG are medians

a.

b. If RG = 24 then GA =

c. If AW = 3, then KA =

d. If MA = 8, then PA =

Primary Vocabulary Terms in Ch. 5(New)

5. Altitude (Section 5.4)a. Goes from vertex to be

perpendicular to the opposite side• Note that sometimes this

means you must extend the opposite side for it to be perpendicular

b. Primarily used as the “height” of a triangle when finding area

Primary Vocabulary Terms in Ch. 5(New)

5. Altitude (Section 5.4)a. Theorem 5.9 – Altitude

Concurrency:Altitudes of a triangle meet at a point called the Orthocenter• Orthocenter does not have

any other special properties that we will discuss

Primary Vocabulary Terms in Ch. 5(New)

5. Altitude (Section 5.4)– Determine the area of the

two triangles