Relationship with Triangles

Tutoring on Relationship with Triangles

Learning Objectives:

Understand and apply the Properties of Midsegment of a triangle.

Math Tutoring on Relationship with Triangles


A Midsegment of a triangle is a line segment that connects two midpoints of adjacent sides of a triangle.Every triangle has three Midsegments.

Properties of Midsegments:

The Midsegment of a triangle joins the midpoints of two sides of a triangle such that the Midsegment is parallel to the third side of the triangle.

Perpendicular Bisectors of the Sides of a Triangle:

The Circumcenter is the Point of Concurrency for the Perpendicular Bisectors of the sides of a triangle.The Circumcenter is the center of a circle that passes through the vertices of the triangle.The Circumcenter is equidistant to the vertices.

Angle Bisector:

There are three Angle Bisectors for a triangle. The Point of Concurrency is called the Incenter. The Incenter is equidistant from the three sides of the triangle. The Incenter is the center of an inscribed circle.


The Median is a line segment that joins a Vertex and the midpoint of the opposite side of a triangle. The Centroid is the center of mass of an object of uniform density in the shape of the triangle.The object would balance on any line through the Centroid.

Concurrency of Medians Theorem:

The Medians intersect in a point that is two-thirds the distance from the vertices to the midpoint on the opposite side.


The Altitude is a line segment from a Vertex that is perpendicular to the opposite side.A triangle has three altitudes.The Point of Concurrency is called the Orthocenter. The Orthocenter can be inside, on or outsides the triangle based upon the type of triangle.

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Hook questions:

1.    What are the Midsegment, Angle Bisector, Median &Altitude of a triangle?

2.   Define the Theorem of Concurrency of Medians?


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