A web page and interactive applet that illustrate the concept of locus. The applet shows a model of the plane populated with a large number of points on a grid. Those points equidistant form a point are highlighted, forming a circle in this case. The user can drag the point and drag the distance, showing the circle moving and changing size. The text page has a description of the locus concept and links to other loci - a straight line and an ellipse. 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 major and minor axes of an ellipse. The applet has an ellipse whose major and minor axis endpoints can be dragged. As they are dragged the major and minor axes change length and may swap places. The applet also shows the location of the foci, which are always on the major axis, and shows how they move with variation of the axis 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.

A free web based math / scientific calculator specially designed for the education environment. It operates in a very similar way to the popular school calculators and so does not need re-learning. The calculator can be blown up to full screen size, making it a useful teaching tool in a classroom setting with a projector. Functions: sin, cos, tan, sin-1, cos-1,tan-1 square root, log10, loge, power of ten, squared, ex Constants: pi, e, root 2 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 medians of a triangle. The applet shows a triangle where the user can drag the vertices to reshape it. As the triangle is being reshaped, the user can see the three median lines tracking the changes, and observe that that all three always intersect at a point inside the triangle. The page text explains that this point of intersection is also the centroid of the triangle, and explains how to determine the location of the medians. 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 midpoint of a line segment. The applet shows a line segment that can be resized and moved using draggable endpoints. The applet always shows the midpoint of the changing line segment. 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 find the midpoint of a line segment when the coordinates of the endpoints are given. The applet has two points on a Cartesian plane. As the user drags either point it continuously recalculates the midpoint of the line segment defined by them. The midpoint is shown both on the plane and as a continuously changing formula. The grid, axis pointers and coordinates can be turned on and off. The midpoint 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 method for finding the midpoint, 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.

A web page and interactive applet illustrating the properties of a nonagon (9 sided polygon). The applet shows a nonagon where the user can drag any vertex to reshape it. User can see that the interior and exterior angles are constant in a regular nonagon, but vary in an irregular version. Controls allow the display or hiding of the diagonals, and triangles within the nonagon. The web page lists the properties of a nonagon 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 obtuse angles (those between 90 and 180 deg). The applet presents an angle (initially obtuse) 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 demonstrate the three types of triangle: acute, obtuse and right. The applet shows a triangle that is initially obtuse (one angle greater than 90 degrees) which the user can reshape by dragging any vertex. There is a message changes in real time while the triangle is being dragged that tells if the triangle is an acute, right or obtuse triangle and gives the reason why. By experimenting with the triangle student can develop an intuitive sense of the difference between these three classes of 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.

A web page and interactive applet illustrating the properties of a octagon (8 sided polygon). The applet shows an octagon where the user can drag any vertex to reshape it. User can see that the interior and exterior angles are constant in a regular octagon, but vary in an irregular version. Controls allow the display or hiding of the diagonals, and triangles within the octagon. The web page lists the properties of an octagon 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 opposite rays. The applet shows two rays with a common endpoint and can be dragged with the mouse. If the rays are in a line, the message 'Opposite rays' appears. A detent makes it easier to get them perfectly aligned. 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 orthocenter of a triangle. The applet shows a triangle where the user can drag the vertices around. The orthocenter and the altitude lines that generate it are continuously moved as the user drags the vertices. By experimentation the user can observe that the orthocenter can be inside or outside the triangle. The page text explains the definition of the orthocenter and how to find 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 concept of parallel lines. The applet shows two lines, one of which has draggable endpoints. As the line is changed by dragging them, the other line changes to remain parallel to 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 properties of parallel lines in coordinate geometry. The applet presents two lines, each defined by a pair of draggable points. If they are parallel the slopes are the same and the applet adds the parallel arrow marks to them. The slope of each line is continuously recalculated and the case of vertical lines (with undefined slope) is handled correctly. The is a software 'detent' that snaps the lines to parallel if they are close to it. The grid, axis pointers and coordinates can be turned on and off. The slope 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 method for determining if lines are parallel, 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.

A web page and interactive applet showing the definition and properties of a parallelogram. The applet shows a parallelogram where the user can drag any vertex. The other points then move in such a way that the figure remains a parallelogram at all times. A control to hide the details allows a classroom discussion where students can try to infer what the properties are as it is reshaped by the discussion leader. Text on the page has the formal definition and properties of the parallelogram with links to related pages. A companion page is http://www.mathopenref.com/parallelogramarea.html showing the ways to calculate the area of a parallelogram 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 pentagon (5 sided polygon). The applet shows a pentagon where the user can drag any vertex to reshape it. User can see that the interior and exterior angles are constant in a regular pentagon, but vary in an irregular version. Controls allow the display or hiding of the diagonals, and triangles within the pentagon. The web page lists the properties of a pentagon 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.

A web page and interactive applet show how to compute the perimeter of a kite. A kite is shown that can be resized by dragging its vertices. As you drag, the perimeter is continuously recalculated. Text on the page explains that the perimeter is the sum of the sides. For those who prefer it, in a formula that is given. 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.

A web page and interactive applet show how to compute the perimeter of a parallelogram. A parallelogram is shown that can be resized by dragging its vertices. As you drag, the perimeter is continuously recalculated. Text on the page explains that the perimeter is the sum of the sides. For those who prefer it, in a formula that is given. 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.

A web page and interactive applet show how to compute the perimeter of a polygon. A polygon is shown that can be resized by dragging its vertices. As you drag, the perimeter is continuously recalculated. Text on the page explains that the perimeter is the sum of the sides. For those who prefer it, in a formula that is given. 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.

A web page and interactive applet show how to compute the perimeter of a rectangle. A rectangle is shown that can be resized by dragging its vertices. As you drag, the perimeter is continuously recalculated. Text on the page explains that the perimeter is the sum of the sides. For those who prefer it, in a formula that is given. 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.