An interactive applet and associated web page that have the definition and meaning of 'equidistant' as applied to points. The applet shows to points and another that is equidistant from them no matter how you drag them around. User can also turn on the locus of the equidistant point, illustrating the definition of a line 'the locus of all points equidistant from two others' 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 equilateral triangles (all sides the same length). The applet presents an equilateral triangle where the user can drag any vertex. As the vertex is dragged, the others move automatically to keep the triangle equilateral. The angles are also updated continuously to show that the all interior angles are always 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 describe the Euler line. It shows a triangle whose vertices can be dragged. As you drag them, the centroid, circumcenter and orthocenter move appropriately, showing that they are always collinear, always lying on the Euler line. There are controls to individually turn on the construction lines for each center. This helps visualize the concept since if they are all drawn at once, the diagram would be hopelessly confused. The web page has a full description the Euler line and has links to separate pages which go into each center in depth. Applet can be enlarged to full screen size for use with a classroom projector. Diagram can be printed. 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 that are formed where a transversal crosses two lines. The applet shows the two possible pairs of exterior angles in turn when in animation mode. By dragging the three lines, it can be seen that the angles are supplementary only when the lines are parallel. When not in animated mode, there is a button that alternates the two pairs of angles. The text on the page discusses the properties of the angle pairs both in the parallel and non-parallel cases. 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 center of a circle using any right-angled object, such as a piece of paper. The method uses Thales Theorem to draw two diameters, which intersect at the circle center. 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 instructions on how to find the center of a circle using only a compass and straightedge. The method used involves constructing the perpendicular bisectors of two random chords. The bisectors intersect at the center of the circle. 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 instructions on how to find the foci of a given ellipse using a compass. 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 the definition and properties of the focus points (foci) of an ellipse. The applet has an ellipse whose major and minor axes can be dragged. The applet shows the location of the foci, which are always on the major axis, and shows how they move with variation of the axis lengths. The web page also has a formula for calculating the location of the foci. 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 full angles (those equal to 360 deg). The applet presents an angle (initially full) that the user can adjust by dragging the end points of the line segments forming the angle. As it changes it shows the angle measure and a message that indicate which type of angle it is. There a software 'detents' that make it easy capture exact angles such as 90 degrees and 180 degrees The message and angle measures can be turned off to facilitate classroom discussion. The text on the page has links to other pages defining each angle type in depth. 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 properties the 'Golden Rectangle' whose sides are in the 'golden Ratio' of 1 : 1.618 : 1. The applet shows a golden rectangle whose vertices a re draggable. When dragged the rectangle changes to remain in the that shape. The web page discusses some properties of a golden rectangle and where it appears in art. 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 shows how right triangles that have the hypotenuse and one other leg the same length must be congruent. The applet shows two right triangles, one of which can be reshaped by dragging any vertex. The other changes to remain congruent to it, and the hypotenuse and leg are outlined in bold to show they are the same measure and are the elements being used to prove congruence. 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 heptagon (7 sided polygon). The applet shows a heptagon where the user can drag any vertex to reshape it. User can see that the interior and exterior angles are constant in a regular heptagon, but vary in an irregular version. Controls allow the display or hiding of the diagonals, and triangles within the heptagon. The web page lists the properties of a heptagon 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.

An interactive applet and associated web page that demonstrate how Herons Formula can be used to find the area of a triangle when you know all three sides. A triangle is shown where the user can drag any vertex to reshape it. In real time while dragging, the side lengths change and the formula is recalculated on the screen. The formula can be turned off to facilitate class work. The text on the web page gives the full formula and discusses where is can be applied. 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 hexagon (6 sided polygon). The applet shows a hexagon where the user can drag any vertex to reshape it. User can see that the interior and exterior angles are constant in a regular hexagon, but vary in an irregular version. Controls allow the display or hiding of the diagonals, and triangles within the hexagon. The web page lists the properties of a hexagon 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.

An interactive applet and associated web page that show the definition of a horizontal line in coordinate geometry. The applet has two points that the user can drag which define a line. The line flagged when it is horizontal (slope=0) and the equation of the line is shown. The grid, details and coordinates can be turned on and off. The applet can be printed exactly as it appears on the screen to make handouts. The web page has a discussion on how to test for horizontal, the line equation and has links to other pages relating to coordinate geometry. 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 measure angles using a protractor. Specifically, it uses a protractor to measure two angles that form a vertical pair, verifying they have the same measure. 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 use a protractor to draw an angle. 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 demonstrate the incircle of a polygon - The largest circle the will fit inside a polygon that touches every side. The applet shows a polygon where the user can drag any vertex and change the number of sides. As they do so, the incircle is drawn for that polygon and the radius calculation is updated. Calculation can be turned off for class discussions. The text on the web page gives two formulae for calculating the inradius, depending on the initial givens. 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 inscribed angle of a circle - the angle subtended at the periphery by two points on the circle. The applet presents a circle with three points on it that can be dragged. The inscribed angle is shown and demonstrates that it is constant as the vertex is dragged. Links to other related topics such as Thales Theorem. 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 intercept (b) of a line. The applet has two points that define a line. As the user drags either point it continuously recalculates the intercept, the point where the line crosses the y-axis at x=0. Can be used in conjunction with the slope to derive the equation of a line. The grid, axis pointers and coordinates can be turned on and off. The intercept calculation can be turned off to permit class exercises and then turned back on the verify the answers. The applet can be printed as it appears on the screen to make handouts. The web page has a full description of the concept of intercept, a worked example and has links to other pages relating to coordinate geometry. 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.