An interactive applet and associated web page that demonstrate the circumference of a circle. The applet shows a circle with a radius line. The radius endpoints are draggable and the circle is resized accordingly. The formula relating radius to circumference is updated continually as you drag. Introduces the idea of Pi. The formula can be hidden for class discussion and estimation. See also the entries for circumference and diameter. See also entries for radius and diameter. 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 show the definition and properties of the bounding box of a polygon or set of points. The bounding box is used in other entries to find area using the so-called box method. The grid, coordinates and calculations can be turned on and off for class problem solving. The applet can be printed in the state it appears on the screen to make handouts. The web page has a full definition of a bounding box when the coordinates of the points defining it are known, and has links to other pages relating to coordinate geometry and a worked example. 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 collinear points. Four draggable points are shown. Dragging any one of them will cause the others to move so they are always collinear. A button controls the line that can be drawn through them. 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 complementary angles (angles that add to 90 degrees). The applet shows two angles. You can drag the endpoints of each angle and the other angle changes so that they always add to 90 degrees. They are drawn in such a way that it is visually obvious that together they form a right angle, although they are separate on the page. The angle measure readouts can be turned off for class discussions. 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 a concave polygon - one where at least one interior angle is greater than 180 degrees. The applet shows an irregular polygon initially with one interior angle greater than 180 degrees. The user can drag any vertex and change the number of sides in the range 3..99. When the polygon is concave, the angles that make it so are drawn in red. The goal is to show through experimentation what the concept of concavity really means. 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 concentricity. The applet shows two resizeable concentric circles and the common center point. As they are dragged to resize, they remain concentric. 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 congruent angles. Three angles are shown which always remain congruent as you drag any defining point on any angle. They all change together. This is designed to demonstrate that the angles are considered congruent even if they are in different orientations and the line segments making them up are different lengths. 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 congruence of polygons. The applet presents nine polygons that are in fact congruent, but don't look it because they are reflected and rotated in various ways. If you click on one, it rotates and flips as needed, then slides over the top of another to show it is congruent. The web page describes how to determine if two polygons are congruent. 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 congruent triangles. Applets show that triangles a re congruent if the are the same, rotated, or reflected. In each case the user can drag one triangle and see how another triangle changes to remain congruent 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.

An interactive applet and associated web page that provide step-by-step animated instructions on how to construct a triangle given all three sides (SSS), using only a compass and straightedge. The animation can be run either continuously like a video, or single stepped to allow classroom discussion and thought between steps. 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 provide step-by-step animated instructions on how to construct a triangle given two angles and the included side length (ASA), using only a compass and straightedge. The animation can be run either continuously like a video, or single stepped to allow classroom discussion and thought between steps. 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 provide step-by-step animated instructions on how to construct a triangle given two sides and the included angle (SAS), using only a compass and straightedge. The animation can be run either continuously like a video, or single stepped to allow classroom discussion and thought between steps. 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 provide step-by-step animated instructions on how to construct 30-60-90 triangle with given base length using only a compass and straightedge. The animation can be run either continuously like a video, or single stepped to allow classroom discussion and thought between steps. 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 show how to construct a 30 degrees angle with a compass and straightedge. The animation can be single-stepped or run as a continuous movie. 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 show how to construct a 45 degrees angle with a compass and straightedge. The animation can be single-stepped or run as a continuous movie. 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 show how to construct a 60 degrees angle with a compass and straightedge. The animation can be single-stepped or run as a continuous movie. 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 show how to construct a 90 degrees right angle with a compass and straightedge. The animation can be single-stepped or run as a continuous movie. 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 how to construct the circle that passes through all three given points. The applet starts with three given points and the user can single step or run continuously through the animated construction, ending with the desired circle. The text on the page contains written step-by-step instructions that can be printed. 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 provide step-by-step instructions on how to find the circumcenter and circumcircle of a triangle using only a compass and straightedge. The method used involves constructing the perpendicular bisectors of two of the triangle's sides. The bisectors intersect at the circumcenter of the triangle. The animation can be run either continuously like a video, or single stepped to allow classroom discussion and thought between steps. 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.