An interactive applet and associated web page that demonstrate the properties of ...

An interactive applet and associated web page that demonstrate the properties of a 30-60-90 triangle. The applet shows a right triangle that can be resized by dragging any vertex. As it is dragged, the remaining vertices change so that the triangle's angles remain 30 degrees, 60 degrees and 90 degrees The text on the page points out that the sides of a 30-60-90 triangle are always in the ratio of 1 : 2 : root 3 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 ...

An interactive applet and associated web page that demonstrate the properties of a 3:4:5 triangle - one of the Pythagorean triples. The applet shows a right triangle that can be resized by dragging any vertex. As it is dragged, the remaining vertices change so that the triangle's side remain in the ration 3:4:5. The text on the page has an example of how the triangle can be used to measure a right angle on even large objects. 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 ...

An interactive applet and associated web page that demonstrate the properties of a 45-45-90 isosceles right triangle. The applet shows a right triangle that can be resized by dragging any vertex. As it is dragged, the remaining vertices change so that the triangle's angles remain 45 degrees, 45 degrees and 90 degrees The text on the page points out that the sides of a 45-45-90 triangle are always in the ratio of 1 : 2 : root 2 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 that angle-angle-angle (AAA) ...

An interactive applet and associated web page that shows that angle-angle-angle (AAA) is not enough to prove congruence. The applet shows two triangles, one of which can be dragged to resize it, showing that although they have the same angles they are not the same size and thus not congruent. 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 AAA similarity ...

An interactive applet and associated web page showing how the AAA 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 interior angles congruent). 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 how triangles that ...

An interactive applet and associated web page that shows how triangles that have two angles and a non-included side 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 angles and non-included side 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 that shows how triangles that ...

An interactive applet and associated web page that shows how triangles that have two angles and their included side 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 angles and the included side 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 that demonstrate acute angles (those ...

An interactive applet and associated web page that demonstrate acute angles (those less than 90 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 the three types ...

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 acute (all angles less then 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 show the concept of ...

An interactive applet and associated web page that show the concept of adjacent angles (two angles that share a common leg). The applet shows three line segments with a common endpoint. The user can move the center one and see that the angles on both sides (the adjacent angles) of it are affected. Applet can be enlarged to full screen size for use with a classroom projector. After use in the classroom, students can access it again from any web browser at home or in the library with no login required. 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 the concept ...

An interactive applet and associated web page that demonstrate the the concept of adjacent arcs. The user can 3 drag points around a circle that define the endpoints of two adjacent arcs. Web page has the properties of adjacent arcs. 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 alternate exterior ...

An interactive applet and associated web page that demonstrate the alternate exterior angles that are formed where a transversal crosses two lines. The applets shows the two possible pairs of angles alternating when in animation mode. By dragging the three lines, it can be seen that the angles are congruent 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 demonstrate the alternate interior ...

An interactive applet and associated web page that demonstrate the alternate interior angles that are formed where a transversal crosses two lines. The applets shows the two possible pairs of angles alternating when in animation mode. By dragging the three lines, it can be seen that the angles are congruent 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 introduce the concept of ...

An interactive applet and associated web page that introduce the concept of an angle. An angle made from two line segments is shown that the user can adjust by dragging the end points of the segments. In real time, as the angles is changed by the user, the angle measure in degrees is shown and a message telling what type of angle it currently is: acute, right, obtuse, reflex or straight. 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 bisector of ...

An interactive applet and associated web page that demonstrate the bisector of an angle. An angle is shown using two line segments that can be dragged to change the angle measure. The angle is bisected by a line which moves while dragging to always divide the angle into two equal angles. The angle measures 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 that acts as a 'digital manipulative' for explaining angles ...

An interactive applet that acts as a 'digital manipulative' for explaining angles measured in degrees. The applet has an angle formed from two segment that can be dragged around in a circle. The angle measure is shown against a 'clock face' calibrated in degrees. The measures can be turned off for class angle estimation 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 apothem of ...

An interactive applet and associated web page that demonstrate the apothem of a regular polygon. The applet shows a regular polygon where the user can alter the number of sides and resize it by dragging any vertex. At all times, the apothem (line from center to a midpoint of a side) is drawn and it's length shown. The text on the page shows two formulae for calculating the apothem, depending on what you are give to start. 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 ...

An interactive applet and associated web page that demonstrate the concept of an arc. The applet shows a circle with part of it highlighted to identify the arc. Each endpoint of the arc can be dragged to resize it. The web page has definitions and links to the properties of an arc. 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 ...

An interactive applet and associated web page that demonstrate the concept of arc length. The applet shows a circle with part of its circumference highlighted and the central angle shown. As the user drags either end of the arc it is redrawn and the calculation for arc length changes as you drag. The text on the web page gives the formula for calculating the arc length. 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 ...

An interactive applet and associated web page that demonstrate the concept of the peripheral angle (inscribed angle) of an arc. This is the angle subtended at the circle circumference of an arc. The applet shows an arc with draggable end points and the angle it subtends at the circumference. It is seen that this angle is constant for a constant arc length. It shows also what happens when the vertex is inside the arc that subtends it The web page has links to other arc properties and a formula for the subtended angle for a given arc length. 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 ...

An interactive applet and associated web page showing how to find the area and perimeter of a square from the coordinates of its vertices. The square 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 the area of ...

An interactive applet and associated web page that demonstrate the area of a circle. A circle is shown with a point on the circumference that can be dragged to resize the circle. As the circle is resized, the radius and the area computation is shown changing in real time. The radius and formula can be hidden 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 area of ...

An interactive applet and associated web page that demonstrate the area of an ellipse. The major and minor axes can be dragged and the area is continuously recalculated. The ellipse has a grid inside it so that students can estimate the area and compare the result to the calculated one. The web page has the formula for the area calculation. The web page also has 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.

An interactive applet and associated web page that deals with the area ...

An interactive applet and associated web page that deals with the area of a kite, (a quadrilateral with two distinct pairs of equal adjacent sides). The applet shows a kite and the user can reshape it by dragging any vertex. The other vertices move automatically to ensure it always remains a kite. As the vertices are dragged, the area is continuously recalculated and displayed. The kite is filled with a grid of unit squares so that the students can estimate the area. The on-screen calculation can be hidden until the estimates are done. The web page lists two different ways to compute the area of a kite. 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 area of ...

An interactive applet and associated web page that demonstrate the area of 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. As you drag the endpoints, the area is continuously recalculated. The calculation can be turned off for class discussions. The web page has the formula for the area. 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 area ...

A web page and interactive applet show how to compute the area of an annulus. Text on the page explains that the area is the overall area minus the area of the circular 'hole' in the center. For those who prefer it in a formula that is given. The user can resize the two circles defining the annulus and visually estimate the area from a unit grid drawn inside it. A companion page is Definition of an Annulus at http://www.mathopenref.com/annulus.html 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 ...

A web page and interactive applet showing the ways to calculate the area of a parallelogram. The user can drag the vertices of the parallelogram and the other points change automatically to ensure it remains a parallelogram. A grid inside the shape allows students to estimate the area visually, then check against the actual computed area, which is continuously recomputed and displayed. 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/parallelogram.html showing the definition and properties 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 showing the ways to calculate the ...

A web page and interactive applet showing the ways to calculate the area of a rectangle. The user can drag the vertices of the rectangle and the other points change automatically to ensure it remains a rectangle. 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 rectangle is reshaped with the mouse. A companion page is http://www.mathopenref.com/rectangle.html showing the definition and properties 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 demonstrate the area of ...

An interactive applet and associated web page that demonstrate the area of a square. The applet shows a square with all vertices draggable. As you drag any one, the area id continuously calculated and shown on the applet. The square is filled with a unit grid to allow class estimation of area. The displayed calculation can be turned off. 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 ...

A web page and interactive applet showing the ways to calculate the area of a trapezoid. The user can drag the vertices of the trapezoid and the other points change automatically to ensure it remains a trapezoid. 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 trapezoid is reshaped with the mouse. A companion page is http://www.mathopenref.com/trapezoid.html showing the definition and properties of a trapezoid. 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 calculate the area of ...

An interactive applet and associated web page that calculate the area of a triangle using the formula method in coordinate geometry. The applet has a triangle with draggable vertices. As you drag them the triangle's area is recalculated from the vertex coordinates using the formula. The grid and coordinates can be turned on and off. The area 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 using the formula method, 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 explain the area of ...

An interactive applet and associated web page that explain the area of a triangle. The applet shows a triangle that can be reshaped by dragging any vertex. As it changes, the area is continually recalculated using the 'half base times height' method. The triangle has a fixed square grid in its interior that can be used to visually estimate the area for later correlation with the calculated value. The calculation can be hidden while estimation is in progress. The text page has links to a similar page that uses Heron's Formula to compute the area. 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 calculate the area of ...

An interactive applet and associated web page that calculate the area of a triangle using the box method in coordinate geometry. The applet has a triangle with draggable vertices. As you drag them the triangle's bounding box is shown and the area recalculated by subtracting the areas of the outside triangles. The grid and coordinates can be turned on and off. The area 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 using the box method, 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 provide step-by-step instructions on ...

An interactive applet and associated web page that provide step-by-step instructions on how to bisect a line 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 instructions on ...

An interactive applet and associated web page that provide step-by-step instructions on how to bisect an angle 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 the definition of the ...

An interactive applet and associated web page that the definition of the center of a regular polygon. The applet presents a regular polygon, where the user can drag any vertex to resize it, and change the number of sides. The center point is shown to always be the point equidistant from every vertex. 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 define and illustrate the ...

An interactive applet and associated web page that define and illustrate the central angle of a polygon. The applet shows the angle and users can experiment by changing the number of sides and resizing the polygon. The web page has a description and a formula for the central angle given the number of sides. 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 central angle ...

An interactive applet and associated web page that demonstrate the central angle of a circle - the angle subtended at the center by two points ion the circle. The applet presents a circle with two points on it that can be dragged. The central angle is shown changing 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 demonstrate a chord of ...

An interactive applet and associated web page that demonstrate a chord of a circle. The applet shows a circle and two draggable points on its periphery, with the chord drawn between them. A command button turns on the perpendicular bisector of the chord. As you drag the chord about, you can see that the perpendicular bisector always passes through the center of the circle. 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 defining a circle. The applet ...

An interactive applet and associated web page defining a circle. The applet shows a circle where the user can drag the center and a point on the circle. The radius line supports the definition that all points on the circle are a fixed distance from the center. The web page has the definitions of all the circle-related objects, such as diameter, chord etc, with links for each. 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.

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