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.
This lesson unit is intended to help teachers assess how well students …
This lesson unit is intended to help teachers assess how well students are able to: work with concepts of congruency and similarity, including identifying corresponding sides and corresponding angles within and between triangles; Identify and understand the significance of a counter-example; Prove, and evaluate proofs in a geometric context.
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.
This task provides a construction of the angle bisector of an angle …
This task provides a construction of the angle bisector of an angle by reducing it to the bisection of an angle to finding the midpoint of a line segment. It is worth observing the symmetry -- for both finding midpoints and bisecting angles, the goal is to cut an object into two equal parts. The conclusion of this task is that they are, in a sense, of exactly equivalent difficulty -- bisecting a segment allows us to bisect and angle (part a) and, conversely, bisecting an angle allows us to bisect a segment (part b). In addition to seeing how these two constructions are related, the task also provides an opportunity for students to use two different triangle congruence criteria: SSS and SAS.
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.
We use the derivative to determine the maximum and minimum values of …
We use the derivative to determine the maximum and minimum values of particular functions (e.g. cost, strength, amount of material used in a building, profit, loss, etc.).Differentiation is also used in analysis of finance and economics.
This lesson unit is intended to help you assess how well students …
This lesson unit is intended to help you assess how well students are able to use geometric properties to solve problems. In particular, it will support you in identifying and helping students who have the following difficulties: Solving problems relating to using the measures of the interior angles of polygons; and solving problems relating to using the measures of the exterior angles of polygons.
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.
The famous story of Archimedes running through the streets of Syracuse (in …
The famous story of Archimedes running through the streets of Syracuse (in Sicily during the third century bc) shouting ''Eureka!!!'' (I have found it) reportedly occurred after he solved this problem. The problem combines the ideas of ratio and proportion within the context of density of matter.
This learning video deals with a question of geometrical probability. A key …
This learning video deals with a question of geometrical probability. A key idea presented is the fact that a linear equation in three dimensions produces a plane. The video focuses on random triangles that are defined by their three respective angles. These angles are chosen randomly subject to a constraint that they must sum to 180 degrees. An example of the types of in-class activities for between segments of the video is: Ask six students for numbers and make those numbers the coordinates x,y of three points. Then have the class try to figure out how to decide if the triangle with those corners is acute or obtuse.
In this problem, students are given a picture of two triangles that …
In this problem, students are given a picture of two triangles that appear to be similar, but whose similarity cannot be proven without further information. Asking students to provide a sequence of similarity transformations that maps one triangle to the other focuses them on the work of standard G-SRT.2, using the definition of similarity in terms of similarity transformations.
This short video and interactive assessment activity is designed to give fourth …
This short video and interactive assessment activity is designed to give fourth graders an overview of composite figures composed of squares and rectangles.
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.
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