# Keywords: Plane Geometry (270)

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# SSA doesn't work

An interactive applet and associated web page that shows that side-side-angle is ... (more)

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. (less)

Subject:
Mathematics and Statistics
Material Type:
Simulations
Collection:
Math Open Reference
Provider:
Math Open Reference
Author:
John Page
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# SSS Congruent Triangles

An interactive applet and associated web page that shows how triangles that ... (more)

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. (less)

Subject:
Mathematics and Statistics
Material Type:
Simulations
Collection:
Math Open Reference
Provider:
Math Open Reference
Author:
John Page
Read the Fine Print

# SSS Triangle similarity test

An interactive applet and associated web page showing how the SSS similarity ... (more)

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. (less)

Subject:
Mathematics and Statistics
Material Type:
Simulations
Collection:
Math Open Reference
Provider:
Math Open Reference
Author:
John Page
Read the Fine Print

# Scalene triangle

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

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. (less)

Subject:
Mathematics and Statistics
Material Type:
Simulations
Collection:
Math Open Reference
Provider:
Math Open Reference
Author:
John Page
Read the Fine Print

# Secant

An interactive applet and associated web page that demonstrate a secant to ... (more)

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. (less)

Subject:
Mathematics and Statistics
Material Type:
Simulations
Collection:
Math Open Reference
Provider:
Math Open Reference
Author:
John Page
Read the Fine Print

# Sector

An interactive applet and associated web page that demonstrate a sector - ... (more)

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. (less)

Subject:
Mathematics and Statistics
Material Type:
Simulations
Collection:
Math Open Reference
Provider:
Math Open Reference
Author:
John Page
Read the Fine Print

# Segment of a Circle

An interactive applet and associated web page that demonstrate a segment of ... (more)

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. (less)

Subject:
Mathematics and Statistics
Material Type:
Simulations
Collection:
Math Open Reference
Provider:
Math Open Reference
Author:
John Page
Read the Fine Print

# Semi-major / semi-minor axis of an ellipse

An interactive applet and associated web page that show the semi-major and ... (more)

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. (less)

Subject:
Mathematics and Statistics
Material Type:
Simulations
Collection:
Math Open Reference
Provider:
Math Open Reference
Author:
John Page
Read the Fine Print

# A Shard or Two : How Big was the Plate?

This online activity offers students a chance to apply the concept of ... (more)

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. (less)

Subject:
Mathematics and Statistics
Material Type:
Activities and Labs
Homework and Assignments
Collection:
Figure This!
Provider:
National Council of Teachers of Mathematics (NCTM)
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# Sides of a Polygon

An interactive applet and associated web page that demonstrate congruent line segments ... (more)

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. (less)

Subject:
Mathematics and Statistics
Material Type:
Simulations
Collection:
Math Open Reference
Provider:
Math Open Reference
Author:
John Page
Read the Fine Print

# Similar Triangles

An interactive applet and associated web page that demonstrate the concept of ... (more)

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. (less)

Subject:
Mathematics and Statistics
Material Type:
Simulations
Collection:
Math Open Reference
Provider:
Math Open Reference
Author:
John Page
Read the Fine Print

# Similar polygons and triangles defined

An interactive applet and associated web page that demonstrate the concept of ... (more)

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. (less)

Subject:
Mathematics and Statistics
Material Type:
Simulations
Collection:
Math Open Reference
Provider:
Math Open Reference
Author:
John Page
Read the Fine Print

# Slope (m) of a line (Coordinate Geometry)

An interactive applet and associated web page that demonstrate the slope (m) ... (more)

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. (less)

Subject:
Mathematics and Statistics
Material Type:
Simulations
Collection:
Math Open Reference
Provider:
Math Open Reference
Author:
John Page
Read the Fine Print

# Square and its properties (Coordinate Geometry)

An interactive applet and associated web page that show the definition and ... (more)

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. (less)

Subject:
Mathematics and Statistics
Material Type:
Simulations
Collection:
Math Open Reference
Provider:
Math Open Reference
Author:
John Page
Read the Fine Print

# Squares, Diagonals, and Square Roots

In this lesson, students measure the sides of many squares and their ... (more)

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. (less)

Subject:
Mathematics and Statistics
Material Type:
Activities and Labs
Lesson Plans
Teaching and Learning Strategies
Collection:
Illuminations
Provider:
National Council of Teachers of Mathematics
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# Straight Angle

An interactive applet and associated web page that demonstrate straight angles (those ... (more)

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. (less)

Subject:
Mathematics and Statistics
Material Type:
Simulations
Collection:
Math Open Reference
Provider:
Math Open Reference
Author:
John Page
Read the Fine Print

# Supplementary Angles

An interactive applet and associated web page that demonstrate supplementary angles (two ... (more)

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. (less)

Subject:
Mathematics and Statistics
Material Type:
Simulations
Collection:
Math Open Reference
Provider:
Math Open Reference
Author:
John Page
Read the Fine Print

# Tangent to a circle

An interactive applet and associated web page that demonstrate a tangent to ... (more)

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. (less)

Subject:
Mathematics and Statistics
Material Type: