An interactive applet and associated web page showing how the SSS similarity test works. Two similar triangles are shown that can be resized by dragging. The other triangle adjusts to remain similar and the angle-angle-angle elements are highlighted to show how they are involved in this test of similarity. (all three corresponding sides in the same proportion). 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 reference book project at http://www.mathopenref.com.

An interactive applet and associated web page that demonstrate the properties of scalene triangles. The applet presents a scalene triangle where any vertex can be dragged to reshape it. As it is dragged, the length of the sides and interior angles are continuously changed. If a change is made that causes two sides to be the same length, they are highlighted and the message 'not scalene' appears. The massages and measures can be turned off for class discussions. 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 a secant to a circle. (not trig). The applet shows a circle and a secant line. The points where the secant cross the circle are both draggable. As you drag each, the secant line moves. If you carefully make the two points coincide, it shows a message that this is now a tangent line. 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 a sector - a pie shaped part of a circle. The applet shows a sector against the background of the circle of which it is part. The endpoints of the arc defining it can be dragged and the calculation of the area of the sector is updated continuously. The web page has links to related definitions, and a formula for the area of the sector given its central angle. 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 a segment of a circle - a part of a circle cut off by a chord. The applet shows a circle and a segment of that circle, the ends of which can be dragged to resize the segment. You can create the situation where the chord is a diameter and so no segments are created. 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 semi-major and semi-minor axes of an ellipse. The applet has an ellipse whose major and minor axis endpoints can be dragged. As they are dragged the semi-major and semi-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 semi-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.

This online activity offers students a chance to apply the concept of symmetry to a real archaeology question. The activity calls for a hands-on solution to the initial challenge of determining the size of a plate from only a fragment or shard. Related math questions offer the opportunity to think about lines of symmetry for a variety of shapes. The activity is one of 80 mathematical challenges featured on the Figure This! web site, where real-world uses of mathematics are emphasized. The activity features a solution hint, the solution, and a family activity for investigating lines of symmetry.

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 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.

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.

An interactive applet and associated web page that demonstrate the slope (m) of a line. The applet has two points that define a line. As the user drags either point it continuously recalculates the slope. The rise and run are drawn to show the two elements used in the calculation. 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 concept of slope, 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.

An interactive applet and associated web page that show the definition and properties of a square when applied in coordinate geometry. The applet has a square, and the user can drag any vertex to resize it. It shows how to calculate the side lengths and diagonal length given the vertex coordinates. The grid and coordinates can be turned on and off. The applet can be printed as it appears on the screen to make handouts. The web page has a full definition of a square when the coordinates of the points defining it are known, 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.

In this lesson, students measure the sides of many squares and their diagonals, then consider the ratio of diagonal length to side length. They can note that in all cases the ratio hovers near 1.4 or the square root of 2. The very complete lesson plan contains handouts, questions for discussion, and problems for applying the new learning.

An interactive applet and associated web page that demonstrate straight angles (those equal to 180 deg). The applet presents an angle (initially acute) 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 supplementary angles (two angles that add to 180 degrees.) The applet shows two angles which, while not adjacent, are drawn to strongly suggest visually that they add to a straight angle. Any point defining the angle scan be dragged, and as you do so, the other angle changes to remain supplementary to the one you change. 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 a tangent to a circle. (not trig). The applet shows a circle and a tangent line. The center point and the tangent contact point are both draggable. As you drag each, the figure changes to ensure that the line is always tangential to the circle. The line from the center to the tangent point is shown and the angle is shown to be always 90 degrees no matter what you do. The perpendicular and its angle can be turned off for class discussion. 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 tangent to an ellipse. An ellipse is shown and a tangent line that touches it at the one point. The user can drag the tangent point around the ellipse and the tangent follows. The ellipse can be reshaped by dragging the foci. The applet shows the fact that the two lines from the foci to the tangent meet it at equal angles. The web page has the written properties of the tangent and links to other pages defining the various properties of an ellipse and to some ellipse constructions. 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.

A web page and interactive applet illustrating Thales Theorem (the diameter of a circle always subtends a right angle to any point on the circumference). The applet shows a circle where the user can rotate the diameter and a move a point on the circumference. The applet continuously shows the resulting right triangle, demonstrating that the theorem holds no matter how the points are moved around. Text on the page defines the theorem and relates it to other geometric entities. 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.