Objective: Construction of the incenter. Warm up 1. Identify a median of the triangle. a. b.

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Presentation transcript:

Objective: Construction of the incenter. Warm up 1. Identify a median of the triangle. a. b.

Angle Bisector

1

Point of concurrency: Point where three or more lines meet.

Incenter: Point of concurrency at the interception of the three angle bisectors.

Example 1 Construct the incenter of the given triangle. Located at intersection of angle bisectors.

incenter

1a. Inscribe circle of the triangle using the incenter as the center of the circle. Use the the shortest distance from the incenter to any of the sides of the triangle as the radius of the circle.

Investigation: Write the definition of an altitude?

2. Construct the orthocenter of the given triangle. Located at intersection of the altitudes.

orthocenter

3. Construct the circumcenter. Located at the intersection of the perpendicular bisectors. (constructions)

Circumcenter

3a. Circumscribe circle of triangle using the circumcenter as the center of circle. Use the distance from the circumcenter to any of the vertices on the triangle as the radius.

4.Construct the centroid of the triangle. Located at the intersection of medians. It is the consider the center of gravity of the triangle.

Centroid (center of gravity of the triangle)

1. Define the following terms. a. Medians

Assignment: Carnegie Learning Workbook: Pg 169 #1-4 (constructions)

Notebook Check #1 1._______08/29/14 Investigation: Which angles are congruent? 2._______09/04/14 Investigation: Finding the right bisector. 3._______09/09/14 Investigation: Angle bisecting with a compass. 4._______09/16/14 Investigation: Transformations on a coordinate plane. 5._______09/23/14 Investigation: Dilations on the coordinate plane. 6. ______09/29/14 Objective: Review transformations and symmetry.