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• CCSS.Math.Content.HSG-SRT.B.5 - Use congruence and similarity criteria for triangles to solve problems...
• CCSS.Math.Content.HSG-SRT.B.5 - Use congruence and similarity criteria for triangles to solve problems...
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This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Is the quadrilateral with vertices $(-6, 2)$, $(-3,6)$, $(9, -3)$, $(6,-7)$ a rectangle? Explain....

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
03/13/2013
Unrestricted Use
CC BY
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This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Point $B$ is due east of point $A$. Point $C$ is due north of point $B$. The distance between points $A$ and $C$ is $10\sqrt 2$ meters, and \angle BAC... Subject: Mathematics Material Type: Activity/Lab Provider: Illustrative Mathematics Provider Set: Illustrative Mathematics Author: Illustrative Mathematics Date Added: 03/29/2013 Read the Fine Print Rating 0.0 stars 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. Subject: Geometry Mathematics Material Type: Reading Simulation Provider: Math Open Reference Author: John Page Date Added: 02/16/2011 Only Sharing Permitted CC BY-NC-ND Rating 0.0 stars 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. Subject: Geometry Mathematics Material Type: Assessment Lesson Plan Provider: Shell Center for Mathematical Education Provider Set: Mathematics Assessment Project (MAP) Date Added: 04/26/2013 Only Sharing Permitted CC BY-NC-ND Rating 0.0 stars 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. Subject: Geometry Mathematics Material Type: Assessment Lesson Plan Provider: Shell Center for Mathematical Education Provider Set: Mathematics Assessment Project (MAP) Date Added: 04/26/2013 Unrestricted Use CC BY Rating 0.0 stars This task asks students to use similarity to solve a problem in a context that will be familiar to many, though most students are accustomed to using intuition rather than geometric reasoning to set up the shot. Subject: Geometry Mathematics Trigonometry Material Type: Activity/Lab Provider: Illustrative Mathematics Provider Set: Illustrative Mathematics Author: Illustrative Mathematics Date Added: 08/21/2012 Only Sharing Permitted CC BY-NC-ND Rating 0.0 stars This lesson unit is intended to help teahcers assess how well students solve problems involving measurement, and in particular, to identify and help students who have the following difficulties; computing measurements using formulas; decomposing compound shapes into simpler ones; using right triangles and their properties to solve real-world problems. Subject: Geometry Mathematics Material Type: Assessment Lesson Plan Provider: Shell Center for Mathematical Education Provider Set: Mathematics Assessment Project (MAP) Date Added: 04/26/2013 Read the Fine Print Rating 0.0 stars An interactive applet and associated web page that demonstrate the concept of congruent triangles. Applets show that triangles a re congruent if the are the same, rotated, or reflected. In each case the user can drag one triangle and see how another triangle changes to remain congruent 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. Subject: Geometry Mathematics Material Type: Reading Simulation Provider: Math Open Reference Author: John Page Date Added: 02/16/2011 Unrestricted Use CC BY Rating 0.0 stars This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Rhianna has learned the SSS and SAS congruence tests for triangles and she wonders if these tests might work for parallelograms. SupposeABCD$and$EF...

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/28/2013
Unrestricted Use
CC BY
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This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Three unit squares and two line segments connecting two pairs of vertices are shown. What is the area of $\triangle ABC$?...

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
03/27/2013
Unrestricted Use
CC BY
Rating
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This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Below is a picture of a triangle $ABC$ on the coordinate grid. The red lines are parallel to $\overleftrightarrow{BC}$: Suppose $P = (1.2,1.6)$, Q = (... Subject: Mathematics Material Type: Activity/Lab Provider: Illustrative Mathematics Provider Set: Illustrative Mathematics Author: Illustrative Mathematics Date Added: 01/06/2014 Unrestricted Use CC BY Rating 0.0 stars This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: In rectangleABCD$,$|AB|=6$,$|AD|=30$, and$G$is the midpoint of$\overline{AD}$. Segment$AB$is extended 2 units beyond$B$to point$E$, and$F... Subject: Mathematics Material Type: Activity/Lab Provider: Illustrative Mathematics Provider Set: Illustrative Mathematics Author: Illustrative Mathematics Date Added: 03/27/2013 Unrestricted Use CC BY Rating 0.0 stars This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Suppose we take a square piece of paper and fold it in half vertically and diagonally, leaving the creases shown below: Next a fold is made joining the... Subject: Mathematics Material Type: Activity/Lab Provider: Illustrative Mathematics Provider Set: Illustrative Mathematics Author: Illustrative Mathematics Date Added: 10/30/2013 Unrestricted Use CC BY Rating 0.0 stars This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Milong and her friends are at the beach looking out onto the ocean on a clear day and they wonder how far away the horizon is. About how far can Milong... Subject: Mathematics Material Type: Activity/Lab Provider: Illustrative Mathematics Provider Set: Illustrative Mathematics Author: Illustrative Mathematics Date Added: 10/30/2013 Unrestricted Use CC BY Rating 0.0 stars This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: In the picture below, pointsA$and$B$are the centers of two circles and they are collinear with point$C$. Also$D$and$E\$ lie on the two respecti...

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
10/30/2013
Conditional Remix & Share Permitted
CC BY-NC-SA
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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
07/03/2014
Only Sharing Permitted
CC BY-NC-ND
Rating
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This lesson unit is intended to help teachers assess how well students are able to use geometric properties to solve problems. In particular, the lesson will help you identify and help students who have the following difficulties: solving problems by determining the lengths of the sides in right triangles; and finding the measurements of shapes by decomposing complex shapes into simpler ones. The lesson unit will also help students to recognize that there may be different approaches to geometrical problems, and to understand the relative strengths and weaknesses of those approaches.

Subject:
Geometry
Mathematics
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
Provider Set:
Mathematics Assessment Project (MAP)
04/26/2013
Only Sharing Permitted
CC BY-NC-ND
Rating
0.0 stars

This lesson unit is intended to help teachers assess how well students are able to use geometric properties to solve problems. In particular, it will help you identify and help students who have difficulty: decomposing complex shapes into simpler ones in order to solve a problem; bringing together several geometric concepts to solve a problem; and finding the relationship between radii of inscribed and circumscribed circles of right triangles.

Subject:
Geometry
Mathematics
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
Provider Set:
Mathematics Assessment Project (MAP)
04/26/2013
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

The goal of this task is to provide an opportunity for students to apply a wide range of ideas from geometry and algebra in order to show that a given quadrilateral is a rectangle. Creativity will be essential here as the only given information is the Cartesian coordinates of the quadrilateral's vertices. Using this information to show that the four angles are right angles will require some auxiliary constructions. Students will need ample time and, for some of the methods provided below, guidance. The reward of going through this task thoroughly should justify the effort because it provides students an opportunity to see multiple geometric and algebraic constructions unified to achieve a common purpose.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
05/03/2023
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
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(Nota: Esta es una traducción de un recurso educativo abierto creado por el Departamento de Educación del Estado de Nueva York (NYSED) como parte del proyecto "EngageNY" en 2013. Aunque el recurso real fue traducido por personas, la siguiente descripción se tradujo del inglés original usando Google Translate para ayudar a los usuarios potenciales a decidir si se adapta a sus necesidades y puede contener errores gramaticales o lingüísticos. La descripción original en inglés también se proporciona a continuación.)

Así como se utilizan movimientos rígidos para definir la congruencia en el Módulo 1, se agregan dilataciones para definir la similitud en el Módulo 2. Para poder discutir la similitud, los estudiantes primero deben comprender claramente cómo se comportan las dilataciones. Esto se hace en dos partes, al estudiar cómo las dilataciones producen dibujos de escala y razonando por qué las propiedades de las dilataciones deben ser ciertas. Una vez que las dilataciones se establecen claramente, se definen transformaciones de similitud y se examinan las relaciones de longitud y ángulo, lo que produce criterios de similitud triangular. Sigue una mirada profunda a la similitud dentro de los triángulos rectos, y finalmente el módulo termina con un estudio de trigonometría del triángulo recto.

Encuentre el resto de los recursos matemáticos de Engageny en https://archive.org/details/engageny-mathematics.

English Description:
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