Visiting the Rich History of Geometry using the TI-92

Published on
07/30/2005

Activity Overview

In this activity, students study various geometric theorems.

Before the Activity

Download TI Connect™ using the TI Connectivity Cable

See the attached PDF file for detailed instructions for this activity

Print pages 1 - 3 from the attached PDF file for your class

During the Activity

Distribute the pages to the class.

Understand the following geometric facts:
Orthocenter:

Given an orthocenter and three vertices of a triangle, any triangle formed by any three of these points will have the fourth point as its orthocenter

Euler Line:

In any triangle, the centroid, orthocenter, and the circumcenter are collinear, and the line is called the Euler line

The distance from the centroid to the orthocenter is twice the distance from the circumcenter to the centroid

Feuerbach Circle:

In any triangle, the midpoints of the sides, the feet of the altitudes, and the midpoints of the segments joining the vertices to the orthocenter all lie on a circle called the Nine Point circle or the Feuerbach Circle

Simpson Line:

Feet of the perpendiculars from any point on the circumcircle of a triangle to the sides of the triangle are collinear, and this line is called the Simpson Line

Midsegment's Theorem:

Segment joining the midpoints of any two sides of a triangle is parallel to and one-half the length of the third side

Varignon's Theorem:

Quadrilateral formed by joining the midpoints of the consecutive sides of any quadrilateral is a parallelogram

Golden Ratio:

A Golden Rectangle is one which can be dissected into a square and a rectangle similar to the original figure

After the Activity

Students answer the questions on the activity sheet.

Review student results:

As a class, discuss questions that appeared to be more challenging