A web page and interactive applet showing the definition and properties of a rectangle. The applet shows a rectangle where the user can drag any vertex. The other points then move in such a way that the figure remains a rectangle 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 rectangle with links to related pages. A companion page is http://www.mathopenref.com/rectanglearea.html showing the ways to calculate the area of a rectangle 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 rectangle in coordinate geometry. The applet has a rectangle with draggable vertices. As the user re-sizes the rectangle the applet continuously recalculates its width, height and diagonals from the vertex coordinates. Rectangle can be rotated on the plane to show the more complex cases. 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 rectangle 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.

An interactive applet and associated web page showing how to find the area and perimeter of a rectangle from the coordinates of its vertices. The rectangle can be either parallel to the axes or rotated. The grid and coordinates can be turned on and off. The area and perimeter 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 area and perimeter, 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 demonstrate reflex angles (greater than 180 deg). The applet presents an angle (initially reflex) 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 regular polygons. The applet presents a regular hexagon initially. The user can drag any vertex, which causes all the others to move in such a way as to keep the polygon regular. There are buttons to change the number of sides from 3 to 99. The apothem and circumradius are shown and continuously updated as you drag 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 relationship between the perimeter and area of a triangle. It shows that a triangle with a constant perimeter does NOT have a constant area. The applet has a triangle with one vertex draggable and a constant perimeter. As you drag the vertex, it is clear that the area varies, even though the perimeter is constant. Optionally, you can see the path traced by the dragged vertex and see that it forms an ellipse. A link takes you to a page where this effect is exploited to construct an ellipse with string and pins. The 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 rhombus. The applet shows a rhombus where the user can drag any vertex. The other points then move in such a way that the figure remains a rhombus 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 rhombus with links to related pages. A companion page is http://www.mathopenref.com/rhombusarea.html showing the ways to calculate the area of a rhombus 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 ways to calculate the area of a rhombus. The user can drag the vertices of the rhombus and the other points change automatically to ensure it remains a rhombus. A grid inside the shape allows students to estimate the area visually, then check against the actual computed area. The text on the page gives three different ways to calculate the area with a formula for each. The applet uses one of the methods to compute the area in real time, so it changes as the rhombus is reshaped with the mouse. A companion page is http://www.mathopenref.com/rhombus.html showing the definition and properties of a rhombus 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 right angle (those equal to 90 deg). The applet presents an angle (initially 90 deg) 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 right (one angle 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.

An interactive applet and associated web page that shows how triangles that have two sides and their included angle the same must be congruent. The applet shows two triangles, one of which can be reshaped by dragging any vertex. The other changes to remain congruent to it and the two sides and the included angle 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.

An interactive applet and associated web page showing how the SAS similarity test works. Two similar triangles are shown that can be resized by dragging. The other triangle adjusts to remain similar and the side-angle-side elements are highlighted to show how they are involved in this test of similarity. (two sides in proportion and the included angle the same). 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 shows that side-side-angle is not enough to prove congruence, because two triangles can meet the condition. The applet shows two triangles, one of which can flip between the two possible configurations that both meet the SSA criteria, showing it is insufficient. 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 shows how triangles that have all 3 sides the same length must be congruent. The applet shows two triangles, one of which can be reshaped by dragging any vertex. The other changes to remain congruent to it and the three sides are outlined in bold to show they are the same length 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.

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.