# Activities

• • • ##### Subject Area

• Math: PreAlgebra: Geometry

• ##### Author 9-12

60 Minutes

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

TI Connect™

• ##### Accessories

TI Connectivity Cable

• ##### Report an Issue

Bring Geometry To Life

#### Activity Overview

In this activity, students use the Geometer's Sketchpad application to construct Euler's Line, Pythagorean Proof, and Fermat's point. They also investigate the concept of perimeter.

#### Before the Activity

• Install the The Geometer's Sketchpad application on the calculator using the TI Connect™ and the TI Connectivity Cable
• See the attached PDF file for detailed instructions for this activity
• Print pages 1 - 8 from the attached PDF file for your class
• #### During the Activity

Distribute the pages to the class.

Euler's Line:

• Construct a triangle using The Geometer's Sketchpad
• Draw the medians of the triangle and find their intersection point (the Centroid)
• Draw the perpendicular bisectors of the triangle and find their intersection point (the Circumcenter)
• Determine the intersection of altitudes (the Orthocenter)
• Join these three points to create the Euler's line
• Drag the vertices of the triangle to investigate the placement of the Euler's Line

• Pythagorean Theorem:
• Construct a right triangle using the Geometer's Sketchpad
• Construct three squares formed by the sides of this triangle
• Translate the small and medium squares into the large square
• Note that the sum of the areas of the two smaller squares equals the area of the large square

• Fermat's Point:
• Create a triangle ABC and plot a point P inside it
• Join the point to the vertices of the triangle
• Mark vertex C as the center of rotation and rotate CP and PA 60° about C
• Construct segment PP' and realize that CPP' is an equilateral triangle

• Perimeter:
• Construct a rectangle and a circle
• Transfer the sum of the lengths of two of the rectangle's sides as the chord of the circle and plot a point on the chord
• Create another chord passing through this point
• Find a rectangle with fixed area but different perimeters
• Understand that the rectangle will have maximum perimeter when the constructed chord is the diameter of the circle
• #### 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