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### Lesson: Points of Concurrency

Author: **Phi N**

Subject Area: **Math**

Grade Level: **9 - 12**

#### Introduction

Students will define, manipulate and draw points of concurrency of a triangle.

#### Goals

Students will be able to compare and contrast incenter, circumcenter, orthocenter and centroid. NCSCOS: Geometry: Competency Goal 2 The learner will use geometric and algebraic properties of figures to solve problems and write proofs. Objective 2.03 Apply properties, definitions, and theorems of two-dimensional figures to solve problems and write proofs: 1. Triangles. 2. Quadrilaterals. 3. Other polygons. 4. Circles.

#### Directions

Click on the link of each activity to find the definition of each point of concurrency. Then, using patty paper, a compass and a straightedge to draw points of concurrency.

#### Background Builder

#### Vocabulary Builder

**Message:**

**Vocabulary Words:**

**concurrent**when three or more lines intersect at one point

**incenter**the point where all three of the angle bisectors of a triangle meet

**circumcenter**the point where all three of the perpendicular bisectors of a triangle meet

**orthocenter**the point where all three altitudes of a triangle meet

**centroid**the point where all three medians of a triangle meet