Use Medians and Altitudes Geometry Section 5.4 Use Medians and Altitudes

Median of a Triangle A segment from the vertex to the midpoint of the opposite side. The point of concurrency is the centroid

Concurrency of Medians of a Triangle 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.

Altitude of a Triangle The perpendicular segment from a vertex to the opposite side or to the line that contains the opposite side.

Altitudes in Obtuse Triangles Two of the altitudes are on the exterior of the triangle

Concurrency of Altitudes of a Triangle The lines containing the altitudes of a triangle are concurrent. The point of concurrency is called the orthocenter

Orthocenter of an Acute Triangle Orthocenter is inside the triangle

Orthocenter of an Obtuse Triangle Orthocenter of an obtuse triangle is outside the triangle

Orthocenter of a Right Triangle Orthocenter of a right triangle is on the triangle

Isosceles Triangle In an isosceles triangle, the perpendicular bisector, angle bisector, median, and altitude from the vertex angle to the base are the same segment.

Equilateral Triangle In an equilateral triangle, the perpendicular bisector, angle bisector, median, and altitude are the same segment

Examples classzone

Assignment Section 5.4 Page 322 Problems #4-10 even, 14, 18-22 even, 26 WEB ON ALTITUDE WEB ON MEDIAN