# Activities

• • • ##### Subject Area

• Math: Geometry: Analytic Geometry

• ##### Author 9-12

60 Minutes

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

TI Connect™

• ##### Accessories

TI Connectivity Cable

## Visiting the Rich History of Geometry using the TI-92

#### Activity Overview

In this activity, students study various geometric theorems.

#### Before the Activity

• 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
• Re-teach concepts as necessary