GSP Project

7/29/2019 GSP Project

1/8

GSP Project!

My project:

My question was what polygons can you construct with GSP and show howyou construct them. I have decided to construst seven polygons. The polygonsare a equilateral triangle, a right triangle,a isosceles right triangle, a rhombus, a

square, a parallogram, and a rectangle.

Procedure:

Equilateral Triangle

Start with two circles see figure 1

then draw a segment connecting the centers of the circes (which are red see

figure 1 above) ,

Then connect the intersection of the two circles with a segment to each circlecenter see figure below. Note: Make sure that both circles are highlighted when
http://lmg08.files.wordpress.com/2009/11/circles-1.jpghttp://lmg08.files.wordpress.com/2009/11/circles-1.jpg


2/8

you are at the intersection. As you can see below I have measured the sie

lengths. This is my extension to this project, i will show calculations to show

the properties of the polygons I construct. Extension: An equilateral triangle hasthree equal sides.

Right Triangle

First draw a line segment I chose to draw mine horizontal see figure below.

Then highlight the line and one of its points and construct a perpendicular line

from the construct menu.

Then draw another segment from the ther point of your first segment to theperpedicular line. This gives you a rigt triangle. Extension: in the figure below
http://lmg08.files.wordpress.com/2009/11/segment-with-perp-line-5.jpghttp://lmg08.files.wordpress.com/2009/11/line-segment-4.jpghttp://lmg08.files.wordpress.com/2009/11/equal-triangle-woth-side-lengths-3.jpghttp://lmg08.files.wordpress.com/2009/11/segment-with-perp-line-5.jpghttp://lmg08.files.wordpress.com/2009/11/line-segment-4.jpghttp://lmg08.files.wordpress.com/2009/11/equal-triangle-woth-side-lengths-3.jpghttp://lmg08.files.wordpress.com/2009/11/segment-with-perp-line-5.jpghttp://lmg08.files.wordpress.com/2009/11/line-segment-4.jpghttp://lmg08.files.wordpress.com/2009/11/equal-triangle-woth-side-lengths-3.jpg


3/8

I measured the angles to show that a right triangle has a 90 degree angle. The

letter H is the right angle in this example.

Isoseles Right Triangle

Draw a circle then connect the center point of the circle to a point on the circle,

see figure below.

Then highlight the center point and the segment and draw a perpendicular line

from the construct menu like before. Then connect the two segments on thecircle. Extension: I have calculated the side lengths and the angle measures to

show that a isosceles right triangle has a 90 degree angle and the two segments

connecting at this angle at the same length.
http://lmg08.files.wordpress.com/2009/11/circle-with-seg-7.jpghttp://lmg08.files.wordpress.com/2009/11/right-triangle-with-90-angle-61.jpghttp://lmg08.files.wordpress.com/2009/11/circle-with-seg-7.jpghttp://lmg08.files.wordpress.com/2009/11/right-triangle-with-90-angle-61.jpg


4/8

Rhombus

Start with two circles like in figure 1 then draw a third circle from one side of

one circle to the center of that same circle see figure below.

Draw one segment connecting the two centers of the two circles then asegment connecting the two centers of the third circle see figure below.

Then connect the intersection of the two outer circles with segments. This is therhombus. Extension: I have measured the side lengths and the angles. Rhombus

have all equal sides.
http://lmg08.files.wordpress.com/2009/11/three-circles-with-segments-101.jpghttp://lmg08.files.wordpress.com/2009/11/three-circles-9.jpghttp://lmg08.files.wordpress.com/2009/11/isosceles-right-triangle-8.jpghttp://lmg08.files.wordpress.com/2009/11/three-circles-with-segments-101.jpghttp://lmg08.files.wordpress.com/2009/11/three-circles-9.jpghttp://lmg08.files.wordpress.com/2009/11/isosceles-right-triangle-8.jpghttp://lmg08.files.wordpress.com/2009/11/three-circles-with-segments-101.jpghttp://lmg08.files.wordpress.com/2009/11/three-circles-9.jpghttp://lmg08.files.wordpress.com/2009/11/isosceles-right-triangle-8.jpg


5/8

Square

Start with two circles line in figure 1 then draw a segment connecting the twocircles line in figure 2 then highlight the segment and one point and construct a

perpendicular line from the construct menu. Do the same for the other point and

the same line segment see figure below.

Then connect the two perpendicular lines where they touch the top of the two

circles. Note: make sure both the circle and the perpendicular line is highlighted

when drawing your segment. The figure below shows the square. Extension:The figure below also shows the side lengths, the angle measures, and a table

showing that even when you change the lengths of the sides the angles also stay

90 degrees.
http://lmg08.files.wordpress.com/2009/11/circles-with-a-segment-and-two-perps-12.jpghttp://lmg08.files.wordpress.com/2009/11/rhombus-with-measurements-11.jpghttp://lmg08.files.wordpress.com/2009/11/circles-with-a-segment-and-two-perps-12.jpghttp://lmg08.files.wordpress.com/2009/11/rhombus-with-measurements-11.jpg


6/8

Parallelogram

First draw a segment, mine is horizontal. Then construct a point and highlight

the point and the segment and construct a parallel line see figure below.

Then draw a segment from the point on the parallel line to the drawn segment.Then highlight the point from the first segment and the newly drawn segmentand construct a parallel line see figure below.

Rectangle

Start with a segment, highlight the segment and a point, construct a

perpendicular line then highlight the segment and the other end point andconstruct another perpendicular line see figure below.
http://lmg08.files.wordpress.com/2009/11/parallelogram-151.jpghttp://lmg08.files.wordpress.com/2009/11/segment-and-para-line-14.jpghttp://lmg08.files.wordpress.com/2009/11/final-square-13.jpghttp://lmg08.files.wordpress.com/2009/11/parallelogram-151.jpghttp://lmg08.files.wordpress.com/2009/11/segment-and-para-line-14.jpghttp://lmg08.files.wordpress.com/2009/11/final-square-13.jpghttp://lmg08.files.wordpress.com/2009/11/parallelogram-151.jpghttp://lmg08.files.wordpress.com/2009/11/segment-and-para-line-14.jpghttp://lmg08.files.wordpress.com/2009/11/final-square-13.jpg


7/8

Draw a point above the segment and between the two parallel lines. Extension:

The figure shows that angle measures are 90 degrees and that a rectangle has

two pairs of sides that are the same length.

Extensions:

My extension was to add side length measurements and angle measurements toeach polygon constructed to show why these are the general polygons, meaning

they will pass the drag test and will always have the same properties.

What I learned:

I learned how to construct different polygons and how to teach someone how to

construct them through writing step by step how to do the constructions. I havelearned how to use other geometrical figures to construct polygons. For

example I used circles to construct many of the polygons.

Implications for the Classroom:

I can use GSP to let my students discover the properties for different polygons.

With GSP they can measure side lengths and different angles and use this to see
http://lmg08.files.wordpress.com/2009/11/rectangle-17.jpghttp://lmg08.files.wordpress.com/2009/11/segment-and-perp-lines-16.jpghttp://lmg08.files.wordpress.com/2009/11/rectangle-17.jpghttp://lmg08.files.wordpress.com/2009/11/segment-and-perp-lines-16.jpg


8/8

the different properties and how they will always hold true for different sizes of

the same polygon. Also I can use GSP myself to make tests and models for my

students to look at. Objectives that can be covered by GSP are:

Demonstrate competency with measurement tools ALCOS 17, Team-Math M1.

Classify types of triangles ALCOS 8, Team-Math G2. Apply angle properties of triangles ALCOS 8, Team-Math G6. Apply properties of parallel lines, similar polygons, and similar triangles

including use of scale factors and proportions ALCOS 3a, 5 Team-MathG2.

Determine the measures of interior and exterior angles associated withpolygons and verify formulas ALCOS 4, 4a, Team-Math M2, M2a

Identify quadrilaterals from verbal descriptions of properties and applyproperties ALCOS 3, 12, Team-Math G1, A1a.

Documents

GSP Project