Education Technology

# Activities

• ##### Subject Area

• Math: Geometry: Triangles

9-12

60 Minutes

• ##### Device
• TI-89 / TI-89 Titanium
• TI-92 Plus / Voyage™ 200

TI Connect™

• ##### Accessories

TI Connectivity Cable

• ##### Other Materials
This is Activity 8 from the EXPLORATIONS Book:
Geometric Investigations on the Voyage 200 with Cabri

## The Simson Line

#### Activity Overview

Students study the Simson line and analyze the relationship it shares with its triangle.

#### Before the Activity

• See the attached PDF file for detailed instructions for this activity
• Print page 43 from the attached PDF file for your class
• #### During the Activity

Distribute the page to the class.

• Draw a triangle and construct its circumcircle
• Place a point P anywhere on the circumcircle and hide the perpendicular bisectors
• Extend the sides of the triangle
• Draw perpendiculars from point P to the extended lines, and label the points of intersection
• Observe that the 3 points are collinear, and understand that the line connecting these 3 points is called Simson Line or Wallace Line
• Realize that if point P is on a vertex of the triangle, then two of the three points of intersection are located at the same vertex
• Create a macro to explore which points on the circumcircle have a Simson line that passes through each of the sides of the triangle
• #### After the Activity

Review student results:

• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary