Learning Objectives:

__Math Tutoring on Relationship with Triangles__

*Midsegment:*

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**.**

*Median:*

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.

*Altitude:*

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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