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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.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
01/11/2013
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CC BY
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The purpose of this task is primarily assessment-oriented, asking students to demonstrate knowledge of how to determine the congruency of triangles.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012
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CC BY
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This task provides the most famous construction to bisect a given angle. It applies when the angle is not 180 degrees.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
01/11/2013
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CC BY
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This task shows that the three perpendicular bisectors of the sides of a triangle all meet in a point, using the characterization of the perpendicular bisector of a line segment as the set of points equidistant from the two ends of the segment. The point so constructed is called the circumcenter of the triangle.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
03/04/2013
Conditional Remix & Share Permitted
CC BY-NC-SA
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Students identify, perform, and algebraically describe rigid motions to establish congruence of two dimensional polygons, including triangles, and develop congruence criteria for triangles.

Subject:
Geometry
Mathematics
Material Type:
Unit of Study
Provider:
Fishtank Learning
Provider Set:
Mathematics
11/19/2021
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CC BY
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This task is designed to give students insight into the effects of translations, rotations, and reflections on geometric figures in the context of showing that two figures are congruent.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
11/12/2012
Unrestricted Use
CC BY
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Students' first experience with transformations is likely to be with specific shapes like triangles, quadrilaterals, circles, and figures with symmetry. Exhibiting a sequence of transformations that shows that two generic line segments of the same length are congruent is a good way for students to begin thinking about transformations in greater generality.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012
Unrestricted Use
CC BY
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This task has two goals: first to develop student understanding of rigid motions in the context of demonstrating congruence. Secondly, student knowledge of reflections is refined by considering the notion of orientation in part (b).

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
12/18/2012
Unrestricted Use
CC BY
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The construction of the perpendicular bisector of a line segment is one of the most common in plane geometry and it is undertaken here. In addition to giving students a chance to work with straightedge and compass, the problem uses triangle congruence both to show that the constructed line is perpendicular to AB and to show that it bisects AB.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
01/11/2013
Educational Use
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This lesson [2:00] will define the phrase corresponding parts (e.g. angles, sides, etc.). It is 1 of 5 in the series titled "Corresponding Parts."

Subject:
Mathematics
Material Type:
Audio/Video
Provider:
Sophia Learning
12/01/2023
Educational Use
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This lesson [4:27] will define the phrase corresponding parts (e.g. angles, sides, etc.). It is 2 of 5 in the series titled "Corresponding Parts."

Subject:
Mathematics
Material Type:
Audio/Video
Provider:
Sophia Learning
12/01/2023
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Use the triangle congruence criteria SSS, SAS, ASA, and AAS to determine that two triangles are congruent. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

Subject:
Mathematics
Material Type:
Audio/Video
Lesson
Provider:
11/14/2023
Educational Use
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Students, teachers, and parents alike will enjoy this challenging math site. It contains a clever brain teaser section plus creative problems related to algebra, geometry, measurement, numbers, statistics, and probability. A Spanish version is available.

Subject:
Mathematics
Material Type:
Lesson
Provider:
National Council of Teachers of Mathematics
Provider Set:
Figure This
04/12/2021
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CC BY
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This task "Uses facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure (7.G.5)" except that it requires students to know, in addition, something about parallel lines, which students will not see until 8th grade.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012
Educational Use
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Explains the basic concept of a rectangle with step-by-step instructions and methods for solving specific problems on your own relating to this topic.

Subject:
Mathematics
Material Type:
Author:
Ido Sarig
11/01/2022
Educational Use
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Explains the basic concept of a square with step-by-step instructions and methods for solving specific problems on your own relating to this topic.

Subject:
Mathematics
Material Type:
Author:
Ido Sarig
11/01/2022
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Module 1 embodies critical changes in Geometry as outlined by the Common Core. The heart of the module is the study of transformations and the role transformations play in defining congruence. The topic of transformations is introduced in a primarily experiential manner in Grade 8 and is formalized in Grade 10 with the use of precise language. The need for clear use of language is emphasized through vocabulary, the process of writing steps to perform constructions, and ultimately as part of the proof-writing process.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Subject:
Geometry
Mathematics
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
05/14/2013
Conditional Remix & Share Permitted
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Just as rigid motions are used to define congruence in Module 1, so dilations are added to define similarity in Module 2.  To be able to discuss similarity, students must first have a clear understanding of how dilations behave.  This is done in two parts, by studying how dilations yield scale drawings and reasoning why the properties of dilations must be true. Once dilations are clearly established, similarity transformations are defined and length and angle relationships are examined, yielding triangle similarity criteria.  An in-depth look at similarity within right triangles follows, and finally the module ends with a study of right triangle trigonometry.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Subject:
Geometry
Mathematics
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY