This concept introduces students to angles, congruent angles, and angle bisectors. Students examine guided notes, review guided practice, watch instructional videos and attempt practice problems.
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In this lesson students determine whether two triangles are congruent. Students examine guided notes, review guided practice, watch instructional videos and attempt practice problems.
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In this lesson students prove two right triangles are congruent with the Hypotenuse-Leg shortcut. Students examine guided notes, review guided practice, watch instructional videos and attempt practice problems.
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This concept introduces the HL Triangle Congruence shortcut in order to prove that two right triangles are congruent. Students work on mastering the skill by watch videos, studying guided notes, reviewing vocabulary, and working on practice problems.
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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.
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.
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.
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.
This module brings together the ideas of similarity and congruence and the properties of length, area, and geometric constructions studied throughout the year. It also includes the specific properties of triangles, special quadrilaterals, parallel lines and transversals, and rigid motions established and built upon throughout this mathematical story. This module's focus is on the possible geometric relationships between a pair of intersecting lines and a circle drawn on the page.
Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.
This study guide reviews proofs: algebraic proof, properties of congruence, and geometric proofs (two-column).
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This concept introduces students to the SAS Triangle Postulate and how to prove that two triangles are congruent given only information about two pairs of sides and the included angles.
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Prove two triangles are congruent with the Side-Angle-Side shortcut.
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Prove two triangles are congruent with the Side-Side-Side shortcut.
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This concept introduces students to the SSS Triangle Congruence Postulate and how to prove that two triangles are congruent given only information about their side lengths.
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In this module, students learn about translations, reflections, and rotations in the plane and, more importantly, how to use them to precisely define the concept of congruence. Throughout Topic A, on the definitions and properties of the basic rigid motions, students verify experimentally their basic properties and, when feasible, deepen their understanding of these properties using reasoning. All the lessons of Topic B demonstrate to students the ability to sequence various combinations of rigid motions while maintaining the basic properties of individual rigid motions. Students learn that congruence is just a sequence of basic rigid motions in Topic C, and Topic D begins the learning of Pythagorean Theorem.
Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.
This task shows how to inscribe a circle in a triangle using angle bisectors. A companion task, ``Inscribing a circle in a triangle II'' stresses the auxiliary remarkable fact that comes out of this task, namely that the three angle bisectors of triangle ABC all meet in the point O.
This task is primarily for instructive purposes but can be used for assessment as well. Parts (a) and (b) are good applications of geometric constructions using a compass and could be used for assessment purposes but the process is a bit long since there are six triangles which need to be constructed.
This task provides an opportunity for students to apply triangle congruence theorems in an explicit, interesting context.
This problem introduces the circumcenter of a triangle and shows how it can be used to inscribe the triangle in a circle. It also shows that there cannot be more than one circumcenter.
This task focuses on a remarkable fact which comes out of the construction of the inscribed circle in a triangle: the angle bisectors of the three angles of triangle ABC all meet in a point.