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Jim Wilson
Department of Mathematics Education

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GSP LESSONS

These are examples of using GSP to present lessons/problems using "show/hide" buttons. The links are to your GSP helper application.

• GSP Lesson 1.
  Given two lines and a point "between" them. Construct all circles through the point and tangent to each of the two lines. The case of intersecting lines is shown here.
• GSP Lesson 2.
  Find the shortest path between two points on opposides of the river when crossing the river must be done on a path perpendicular to the banks.
• GSP Lesson 3.
  Given two circles of different radius that intersect. If E is one point of intersection, construct a line through E that cuts off chords of equal length in the two circles.
• GSP Lesson 4a.
  What is the locus of the midpoint of a line segment of varying length where one end is fixed and the other end moves around a circle?
• GSP Lesson 4b.
  What is the locus of the midpoint of a line segment of varying length where one end is fixed and the other end moves around a triangle? Generalize to movement around any closed path.
• GSP Lesson 4c.
  What is the locus of the midpoint of a line segment of varying length where each end of the segment moves around a circle?
• GSP Lesson 5.
  Given two points A and B on the same side of a line k. If C is a point on K, construct the location of C so that AC + CB is a minimum.
• GSP Lesson 6.
  If the base and area of a triangle are fixed, find the triangle with minimal perimeter.
• GSP Lesson 7a.
  Take any parallelogram and construct squares externally on each side. Prove that the centers of the four sqares are the vertices of a square. Show that the area of this square is always greater than or equal to twice the area of the parallelogram. When is it twice the area?
• GSP Lesson 7b.
  Take any parallelogram and construct squares toward the inside of the parallelogram on each side. Prove that the centers of the four sqares are the vertices of a square. Is there a relationship of the area of this square to the area of the parallelogram.
• GSP Lesson 8.
  Given three line segments that are the lengths of a point E from the vetrices A, B, and C or an equilateral triangle. Construct triangle ABC. What if E was a point outside the triangle?
• GSP Lesson 9.
  Construct a triangle of minimal perimeter inscribed in a given acute triangle.
• GSP Lesson 10.
  In an equilateral triangle ABC, let D be the mid-point of AB and E be the mid-point of AC. Extend DE to intersect the circumcircle at point P. Determine the ratio PC/PA. Determine the ratio DE/DP.
• GSP Lesson 11.
  Construct a circle with center O having perpendicular diameters AB and DC. Take the midpoint M of OC and constuct an arc with center at M through A. The arc intersects OD at N.

Investigate ON/DN.
 
Show that AN is the length of the side of an inscribed pentagon. (i.e., construct the inscribed pentagon, . . . and investigate)

Fixed Angle 

 

 

Trisect

 

 

Rectangle circumscribed about an ellipse. Open first GSP file. Open Second GSP File.