An interactive applet and associated web page that demonstrate that the interior angles of a polygon always add to a number related only to the number of sides. The applet shows a polygon where the user can drag the vertices to reshape it, alter the number of sides, make it convex or concave, regular or irregular. The applet shows the angle summation in real time, demonstrating that only the number of sides affects the total. The text on the web page gives the formula for the total of the interior angles. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

An interactive applet and associated web page that demonstrate the diagonals of a polygon. The applet shows a polygon with the diagonals drawn. The user can drag any vertex, make it regular or irregular, and change the number of sides. The applet continually computes and displays the number of diagonals. The text on the web page has the relevant formulae. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

Students take a close look at truss structures, the geometric shapes that compose them, and the many variations seen in bridge designs in use every day. Through a guided worksheet, students draw assorted 2D and 3D polygon shapes and think through their forms and interior angles (mental “testing”) before and after load conditions are applied. They see how engineers add structural members to polygon shapes to support them under compression and tension, and how triangles provide the strongest elemental shape. A PowerPoint® presentation is provided. This lesson prepares students for two associated activities that continue the series on polygons and trusses.

Students learn about the role engineers play in designing and building truss structures. Simulating a real-world civil engineering challenge, student teams are tasked to create strong and unique truss structures for a local bridge. They design to address project constraints, including the requirement to incorporate three different polygon shapes, and follow the steps of the engineering design process. They use hot glue and Popsicle sticks to create their small-size bridge prototypes. After compressive load tests, they evaluate their results and redesign for improvement. They collect, graph and analyze before/after measurements of interior angles to investigate shape deformation. A PowerPoint® presentation, design worksheet and data collection sheet are provided. This activity is the final step in a series on polygons and trusses.

An interactive applet and associated web page that define and describe the radius of a regular polygon. The applet has a polygon where the user can change the umber of sides and alter the radius by dragging a vertex. The radius is shown with it's length changing accordingly. The web page has formulae for the length of the radius given the number of sides and the apothem or side length. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

An interactive applet and associated web page that demonstrate regular polygons. The applet presents a regular hexagon initially. The user can drag any vertex, which causes all the others to move in such a way as to keep the polygon regular. There are buttons to change the number of sides from 3 to 99. The apothem and circumradius are shown and continuously updated as you drag Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

An interactive applet and associated web page that demonstrate congruent line segments (segments that are the same length). The applet shows three line segments that are the same length. They all have draggable endpoints. As you drag any endpoint the other lines change to remain congruent with the one you are changing. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

An interactive applet and associated web page that demonstrate the concept of similar polygons. Applets show that polygons are similar if the are the same shape and possibly rotated, or reflected. In each case the user can drag one polygons and see how another polygons changes to remain similar to it. The web page describes all this and has links to other related pages. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

A web page and interactive applet illustrating the properties of a tetragon (4 sided polygon). The applet shows a tetragon where the user can drag any vertex to reshape the polygon. User can see that the interior and exterior angles are constant in a regular tetragon, but vary in an irregular version. Controls allow the display or hiding of the diagonals, and triangles within the tetragon. The web page lists the properties of a tetragon including interior angles, exterior angles, sum of exterior angles, area, number of diagonals and number of internal triangles. Links to pages with generalized properties of all polygons. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

Students learn about regular polygons and the common characteristics of regular polygons. They relate their mathematical knowledge of these shapes to the presence of these shapes in the human-made structures around us, especially trusses. Through a guided worksheet and teamwork, students explore the idea of dividing regular polygons into triangles, calculating the sums of angles in polygons using triangles, and identifying angles in shapes using protractors. They derive equations 1) for the sum of interior angles in a regular polygon, and 2) to find the measure of each angle in a regular n-gon. This activity extends students’ knowledge to engineering design and truss construction. This activity is the middle step in a series on polygons and trusses, and prepares students for the Polygon and Popsicle Trusses associated activity.

An interactive applet and associated web page that illustrate the triangles that can be drawn inside a polygon. The applet has a pentagon with the triangles drawn. The user can change the number of sides, and switch between regular / irregular. The vertices are draggable. The text on the page discusses the uses of these triangles. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

A web page and interactive applet illustrating the properties of an undecagon (11 sided polygon). The applet shows an undecagon where the user can drag any vertex to reshape it. User can see that the interior and exterior angles are constant in a regular undecagon, but vary in an irregular version. Controls allow the display or hiding of the diagonals, and triangles within the undecagon. The web page lists the properties of the undecagon including interior angles, exterior angles, sum of exterior angles, area, number of diagonals and number of internal triangles. Links to pages with generalized properties of all polygons. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.