Assignment 5

GSP Script Tools

by Margaret Trandel

I have created script tools for the geometric constructions below. Simply click on the links below to open the individual GSP construction files. You'll need GSP on your computer to participate in this activity. After becoming familiar with the terms, try to create your own script tools. I really enjoyed this assignment and I think you will too!

the point of concurrency of the medians of a triangle.

the point of concurrency of the altitudes of a triangle.

the unique circle which passes through each of a triangle's three vertices.

the center of a circumcircle. It is also the intersection of the perpendicular bisectors of the sides of the circumcircle's triangle.

in a triangle, the point of concurrency of the angle bisectors.

the unique circle which is tangent to each of the triangle's three sides.

the triangle formed by connecting the three medians of a triangle.

the triangle formed by connecting the orthocenter H of a triangle to the halfway points between H and the vertices. .

the triangle formed by connecting the three altitudes of a triangle.

given a point P inside a triangle the pedal triangle of P is the triangle whose polygon vertices are the feet of the perpendiculars from P to the sides of the original triangle.

the center of the circle described below - it turns out to be the midpoint between the orthocenter and circumcenter of the 9 point circle's corresponding triangle.

named for the nine easily constructed points on the circle -start with a triangle - the three feet of the altitudes, the three midpoints of the sides and the 3 euler points (an Euler point is the midpoint between the orthocenter of a triangle and a vertex) are all on the nine point circle.

dividing a line segment into three congruent segments.

a triangle with three equal sides.

a four sided polygon with congruent sides and four right angles.

a triangle with at least two congruent sides.

see orthocenter, centroid, circumcenter and incenter.

the Euler Line triangle centers are circumcenter, centroid and orthocenter.

the golden ratio in a divided segment exists when the ratio of the length of the whole line to the length of the longer segment = the ratio of the longer segment to the shorter segment.

Note: The constructions below are all of regular polygons.

a five-sided polygon.

a six-sided polygon.

an eight-sided polygon.

Thanks for opening the above script tools! Please e-mail me if you'd like to share any gsp script tool files.