An interactive applet and associated web page that demonstrate the concept of similar triangles. Applets show that triangles are similar if the are the same shape and possibly rotated, or reflected. In each case the user can drag one triangle and see how another triangle 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.

Students learn that math is important in navigation and engineering. They learn about triangles and how they can help determine distances. Ancient land and sea navigators started with the most basic of navigation equations (speed x time = distance). Today, navigational satellites use equations that take into account the relative effects of space and time. However, even these high-tech wonders cannot be built without pure and simple math concepts — basic geometry and trigonometry — that have been used for thousands of years.

Working as engineering teams, students design and create model beam bridges using plastic drinking straws and tape as their construction materials. Their goal is to build the strongest bridge with a truss pattern of their own design, while meeting the design criteria and constraints. They experiment with different geometric shapes and determine how shapes affect the strength of materials. Let the competition begin!

An interactive applet and associated web page that introduce the concept of a triangle. The applet shows a triangle where the user can drag the vertices to reshape it. As it is being dragged a base and altitude are shown continuously changing. Demonstrates that the altitude may require the base to be extended. The text on the page lists the properties of a triangle and lists the various triangle types, with links to a definition of each. 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.

The applet shows a triangle which the user can resize by dragging any of its vertices. It shows the three perpendicular bisectors of the sides and the point where they intersect - the circumcenter. These track the changes in the triangle in real time. It shows that the circumcenter may lie outside the triangle. The associated web page describes the properties of the circumcenter and points out that it the center of the triangle's circumcircle. 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 demonstrating the concept of the incenter of a triangle. The applet shows a triangle where the user can drag the vertices around. The incenter and the angle bisector lines that generate it are continuously moved as the user drags the vertices. By experimentation the user can observe that the incenter always remains inside the triangle. The page text explains the definition of the incenter and how to find it. It describes how the incenter is also the center of the incircle of the triangle with a link to that page http://www.mathopenref.com/triangleincenter.html 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 demonstrating the concept of the centroid of a triangle. The applet shows a triangle where the user can drag the vertices around. The centroid and the median lines that generate it are continuously moved as the user drags the vertices. By experimentation the user can observe that the centroid always remains inside the triangle. The page text explains the definition of the centroid and how to find it. It also shows that the centroid is the center of gravity of the triangle. 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 properties of the circumcircle of a triangle. The applet shows a triangle where the user can drag the vertices to reshape it. The circumcircle (the circle that passes through all vertices) is continuously updated as the triangle is resized. The center of the circle (circumcenter) is shown along with the three side bisectors that define it. 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 exterior angles of a triangle. The applet shows a triangle where the user can drag any vertex to reshape it. The exterior angles are shown and a running calculation shows that no matter how you change the triangle, the exterior angles always add up to 360 degrees An exterior angle is equal to the sum of the opposite 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.

A web page and interactive applet demonstrating the concept of the incircle of a triangle - the largest circle the will fit inside a triangle. The applet shows a triangle where the user can drag the vertices around. The incircle is continuously adjusted as the user drags the vertices. By experimentation the user can observe that the three sides of the triangle are always tangents to the incircle. The page text explains the definition of the incircle and how to draw it. It describes how the incenter is the center of the incircle of the triangle with a link to that page http://www.mathopenref.com/triangleincircle.html 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 triangle inequality. The applet shows a triangle where the vertices can be dragged to reshape the triangle It shows that no matter what you do, the longest side is always shorter than the sum of the other two. 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 properties of the interior angles of a triangle. The applet shows a triangle where the user can drag the vertices to reshape it. As it is being changed, the angles are continually updated, along with an expression showing that they always add to 180 degrees 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 demonstrates the midsegment (midline) of a triangle. A triangle is shown that the user can reshape by dragging any vertex. As it is being dragged, the midline changes accordingly. From this can be seen that the midsegment is always parallel to the base and half it's 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.

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.

Students learn about the fundamental strength of different shapes, illustrating why structural engineers continue to use the triangle as the structural shape of choice. Examples from everyday life are introduced to show how this shape is consistently used for structural strength. Along with its associated activity, this lesson empowers students to explore the strength of trusses made with different triangular elements to evaluate the various structural properties.

An interactive applet and associated web page that demonstrate that in similar triangles, the ratio of their areas is the square of the ratio of the sides. As you drag one triangle to resize it, it remains similar to another and the ratios of sides and areas is calculated as you drag. One can be seen to be the square of the other at all times. A slight 'snap-to' effect allows easy selection of integer ratios (2:4 etc). 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 reference book project at http://www.mathopenref.com.

An interactive applet and associated web page that demonstrate that in similar triangles, ten items are always in the same ratio to each other (perimeter, three sides, three altitudes, three medians). As you drag one triangle to resize it, it remains similar to another and the ratios of sides and medians is calculated as you drag. They can be seen to be the same at all times. 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 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.

Students learn about and use a right triangle to determine the width of a "pretend" river. Working in teams, they estimate of the width of the river, measure it and compare their results with classmates.

Students learn about trigonometry, geometry and measurements while participating in a hands-on interaction with LEGO® MINDSTORMS® NXT technology. First they review fundamental geometrical and trigonometric concepts. Then, they estimate the height of various objects by using simple trigonometry. Students measure the height of the objects using the LEGO robot kit, giving them an opportunity to see how sensors and technology can be used to measure things on a larger scale. Students discover that they can use this method to estimate the height of buildings, trees or other tall objects. Finally, students synthesize their knowledge by applying it to solve similar problems. By activity end, students have a better grasp of trigonometry and its everyday applications.