Assignment #5

Creating and Using GSP Scripts

T. Barron

The following list identifies scripts using the Geometer's Sketch Pad (GSP). Selecting ("clicking on") any of the BLUE highlighted names or phrases will allow you to see a construction of the item along with directions for performing your own construction. Linking to each item will also allow you to experiment with each shape if you have Geometer's Sketchpad on your computer. Have Fun!!!!

The centroid of a triangle is the common intersection of the three medians. A median of a triangle is the segment from a vertex to the midpoint of the opposite side. Click here for a GSP picture that shows the centroid of a circle and a GSP script that explains how to construct a centroid of a triangle.

The orthocenter of a triangle is the common intersection of the three lines containing the altitudes. An altitude is a perpendicular segment from a vertex to the line of the opposite side. Click here for a GSP picture that shows the orthocenter of a circle and a GSP script that explains how to construct a orthocenter of a triangle.

The circumcenter of a triangle is the point in the plain equidistant from the three vertices of the triangle. Since, by definition, a point equidistant from two points lies on the perpendicular bisector of the segment determined by the two points, the circumcenter is on the perpendicular bisector of each side of the triangle. Notice that the circumcenter may be outside of the triangle. Click here for a GSP picture that shows the circumcenter of a triangle and a GSP script that explains how to construct a circumcenter of a triangle.

The circumcircle is a circle that inscribes a triangle. The center of a circumcircle is also the circumcenter of a triangle. Click here for a GSP picture that shows the circumcircle of a circle and a GSP script that explains how to construct a circumcircle of a triangle.

The incenter of a triangle is the point on the interior of the triangle that is equidistant from the three sides. Since a point interior to an angle that is equidistant from the two sides of the angle lies on the angle bisector, then the incenter of a triangle is on the angle bisector of each angle of the triangle. Click here for a GSP picture that shows the incenter of a circle and a GSP script that explains how to construct a incenter of a triangle.

The incircle is a circle inscribed in a triangle with the center point as the incenter of the triangle. Click here for a GSP picture that shows the incircle of a circle and a GSP script that explains how to construct a incircle of a triangle.

A Medial Triangle is constructed by drawing any acute triangle and connecting the three midpoints of the sides. Click here for a GSP picture that shows a Medial Triangle and to verify that a medial triangle is similar to the original triangle and one-fourth of the area of the original triangle. Also, click here for a GSP script that explains how to construct a Medial Triangle.

An orthocenter is constructed at the point of intersection of the altitudes of a triangle. The mid-segment triangle of an orthocenter is constructed by adjoining the midpoints of the segments between the orthocenter and the vertices of the triangle. See the characteristics of a triangle that shows an orthocenter with a mid-segment triangle or view a GSP script that explains how to construct and orthocenter of a triangle and a mid-segment triangle.

An Orthic Triangle is constructed by connecting the feet of the altitudes of any acute triangle. Click here for a GSP picture that shows an Orthic Triangle and a GSP script that explains how to construct an Orthic Triangle.

Locate a point inside of a triangle and call this point a pedal point. Construct perpendicular segment between the midpoint on each side of the triangle and the pedal point. Construct a triangle by connecting segments from the intersections of each perpendicular segment from the pedal point and the sides of the triangle. This triangle, constructed from the points of intersection between the perpendicular segments dropped from the pedal point and the sides of the triangle is called a Pedal Triangle. Click here for a GSP picture that shows a Pedal Triangle and a GSP script that explains how to construct Pedal Triangle.

The Nine point circle, named for the nine constructed points on it, has several mathematics properties. Every triangle has a Nine Point Circle which is connected to both it's inscribed circle, circumscribed circle, and Euler Line. Click here for detailed instruction regarding how to construct the center of the Nine Point Circle and and further information regarding the construction.

Trisecting a line segment using GSP is not as easy as it may seem. Click here for a GSP picture that shows a trisection of a line segment and a GSP script that explains how to trisect a line segment.

An Equilateral Triangle is a triangle where the measure of the three sides are equal. Click here for a GSP picture that shows the construction of an Equilateral Triangle, given a side and a GSP script that explains how to construct an Equilateral Triangle, given a side.

A square is a quadrilateral that has four equal sides and four equal angles that all measure 90 degrees. Click here for a GSP picture that shows a construction of a square, given a side and a GSP script that explains how to construct a square, given a side.

An Isoceles Triangle is a triangle that has two equal sides and thus, two angles that have equal measures. Click here for a GSP picture that shows the construction of an Isoceles Triangle, given a side and a GSP script that explains how to construct an Isoceles Triangle.

The triangle centers, H (orthocenter), G (centroid), C (circumcenter), and I (incenter) are constructed individually in the above scripts. Click here for a GSP picture that shows the construction of the four Triangle Centers associated with one triangle and a GSP script that explains how to construct the four centers of a triangle associated with one triangle.

The Euler Line of a triangle is the line that contains the circumcenter (C), orthocenter (H), and centroid (G). Click here for a GSP picture that shows the construction of a the four triangle centers (H, G, C, and I) with Euler Line and a GSP script that explains how to construct a the four triangle centers (H, G, C, and I) with Euler Line.

Divide a segment AB into two parts that form a golden ratio. Click here for a GSP picture that shows the construction of a division of a segment AB into two parts that form a golden ratio and a GSP script that explains how to construct the division.

A pentagon is a five-sided polygon. Click here to see a GSP picture that shows the construction of a pentagon, given a radius and a GSP script that explains how to construct a pentagon, given a radius. Click here to see a GSP construction of a pentagon, given a side of the pentagon or a line segment.

A hexagon is a six-sided polygon. Click here for a GSP picture that shows the construction of a hexagon, given a side and a GSP script that explains how to construct a hexagon, given a side.

An Octagon is an eight-sided polygon. Click here for a GSP picture that shows the construction of an octagon, given a side and a GSP script that explains how to construct an octagon, given a side.