A Brief Introduction to
Geometer’s Sketch Pad (GSP)
Armando M. Martinez-Cruz
Maria Fernandez, Fernando Rodriguez,
Buena Park High School
MDTP CSU Fullerton
Jan. 25, 2006
Outline of the Presentation
• Some comments about GSP
• Getting Started: Some menus and
• Dragging: The Transformation Menu
• Repeating the same construction? No
way! Use a Script
Some Comments about GSP:
• GSP is extremely friendly, powerful and self-
contained, but not perfect.
• The power of GSP lies on the ability to
preserve the properties of Euclidean
constructions when figures are dragged.
• Strong tool for pedagogical purposes.
• Constructions can be copied and pasted in
other program documents (like a word
processor) but they become static.
• Photos can be pasted in GSP docs.
• Mathematical investigations are enticed.
• Also good for analytic geometry.
The tool palette
The Construct Menu
The Transform Menu
Dragging is not a Drag
• The math is underneath
CONSTRUCT a human-like figure using circles and
segments. CONSTRUCT and SELECT (i.e., “MARK”) a
line of reflection, and USE the transform menu to reflect
your figure. Then DRAG some (or all) parts.
Using an iterative tool: A Script
for an Equilateral Triangle
• CONSTRUCT segment AB
• CONSTRUCT a circle with center at A and radius
• CONSTRUCT a circle with center at B and radius
• CONSTRUCT the intersection of two circles. Label
• CONSTRUCT segments AC and BC.
• HIDE auxiliary circles
The Custom Tool
TO CREATE A SCRIPT FOR THE
1) SELECT the vertices and sides of the
2) OPEN the custom tool and select
3) NAME the script
A Problem to Investigate
• Construct a parallelogram ABCD. Construct
outward equilateral triangles (ABE and BCF) on
sides AB and BC. What can you say about
• What if the triangles were inward?
• What if one is inward and the other outward?
• Construct a script for the centroid of a triangle.
• Investigate the following problem: Let P be an
interior point in the convex quadrilateral ABCD.
Let Q, R, S and T be the centroid of triangle ABP,
BCP, CDP and DAP respectively. What can you
say about convex quadrilateral QRST?
Medians of a Triangle
• Let M1, M2, and M3 be the medians of triangle
ABC. Construct a triangle PQR with sides
M1, M2, and M3. Is there a relationship
between the areas of triangles ABC and
Photos and Demonstrations
• With the advent (and friendliness) of technology, a
teacher can combine several pieces to bring life to
the classroom. Consider the case of parabolas.
They appear in many places in life. Here, we will
combine a digital camera and GSP.
• A parabola is the locus of all points that are
equidistant to a fixed point called focus and to a
line called directrix.
• Construct a line L and a point F. Construct a
point Q on L. Construct segment FQ and the
perpendicular to L through Q. Denote this
perpendicular as M. Construct the
perpendicular bisector to segment FQ. Let R
be the intersection of this perpendicular
bisector and line M. Select R, Q and line L. Go
to the CONSTRUCT menu and select Locus. A