Bell ProblemFind the value of x.

5.4 Use Medians and Altitudes

Standards:1. Apply proper techniques to find measures

2. Use representations to communicate mathematical ideas

Median of a Triangle

Median of a triangle- a segment from a vertex to the midpoint of the opposite side

Centroid- point of concurrency of the three medians of a triangle

Concurrency of Medians of a TriangleThe 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.

Ex. There are three paths through a triangular park. Each path goes from the midpoint of one edge to the opposite corner. The paths meet at point P. If SC = 2100 feet, find PS and PC.

Ex. Find the coordinates of the centroid P of ΔABC. A(0, 4), B(3, 10), C(6, -2)

Homework

pg. 322 #3-9, 33-35

Bell Problem

Altitude of a TriangleAltitude of a triangle- the perpendicular segment from a vertex to the opposite side or to the line that contains the opposite side

Concurrency of Altitudes of a TriangleThe lines containing the altitudes of a triangle are concurrent.

The lines containing AF, BE, and CD meet at G.

Orthocenter Orthocenter- the point at which the lines containing the three altitudes of a triangle intersect

Isosceles and Equilateral TrianglesIn an isosceles triangle, the perpendicular bisector, angle bisector, median, and altitude from the vertex angle to the base are all the same segment. In an equilateral triangle, this is true for the special segment from any vertex.

Circumcenter, Centroid, Incenter, or Orthocenter ?

Homework

5.4 Practice B worksheet #2-24 even