## ### Lesson: Points of Concurrency

Author: Phi N
Subject Area: Math

#### 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 Title: Review: Median, Altitude, Angle and Perpendicular Bisectors URL:
Directions: Get with a partner and draw the median, altitude, angle and perpendicular bisectors of a triangle. Then, your group will share with the class how you draw one of the four.

#### 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

### Activity: Incenter

#### Goals

Students will define and manipulate the incenter of a triangle.

#### Directions

Click on the link to and manipulate one of the vertices of the triangle, as directed on the website, to see the location of the incenter.

### Activity: Circumcenter

#### Goals

Students will define and manipulate the circumcenter of a triangle.

#### Directions

Click on the link to and manipulate one of the vertices of the triangle, as directed on the website, to see the location of the circumcenter.

### Activity: Orthocenter

#### Goals

Students will define and manipulate the orthocenter of a triangle.

#### Directions

Click on the link to and manipulate one of the vertices of the triangle, as directed on the website, to see the location of the orthocenter.

### Activity: Centroid

#### Goals

Students will define and manipulate the centroid of a triangle.

#### Directions

Click on the link to and manipulate one of the vertices of the triangle, as directed on the website, to see the location of the centroid.