# MDTP Geom Sktchpd Jan 26 06

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```					ABITGSP

A Brief Introduction to
Armando M. Martinez-Cruz
CSU Fullerton

Maria Fernandez, Fernando Rodriguez,
Paul Sexton
Buena Park High School

MDTP CSU Fullerton
Jan. 25, 2006
Outline of the Presentation

• Getting Started: Some menus and
commands
• Repeating the same construction? No
way! Use a Script
• 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

Dragging is not a Drag

•   Construct
•   Transform
•   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.
INVESTIGATE!
Using an iterative tool: A Script
for an Equilateral Triangle

• CONSTRUCT segment AB
• CONSTRUCT a circle with center at A and radius
AB.
• CONSTRUCT a circle with center at B and radius
AB.
• CONSTRUCT the intersection of two circles. Label
it C.
• CONSTRUCT segments AC and BC.
• HIDE auxiliary circles
The Custom Tool

TO CREATE A SCRIPT FOR THE
TRIANGLE:
1) SELECT the vertices and sides of the
triangle
2) OPEN the custom tool and select
NEW
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
triangle EFD?
• What if the triangles were inward?
• What if one is inward and the other outward?
The Centroid

• 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
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
PQR?
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.
Parabolas
• 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
parabola appears.

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