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Geometry Module 2: Similarity, Proof, and Trigonometry
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Just as rigid motions are used to define congruence in Module 1, ...

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.

Subject:
Geometry
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Math, Grade 7, Unit 4, Lesson 2
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Students find the area of regular polygons, recalling what they already know ...

Students find the area of regular polygons, recalling what they already know about the area of geometric shapes and generalizing a formula for any regular polygon.

Key Concepts

Students will recall what they already know about the area of geometric shapes and apply that to find the area of regular polygons. Any regular polygon can be divided into congruent isosceles triangles. If the length from the center to the midpoint of a side (the apothem ) is known, the area of the triangles and the area of the polygon can be found. Students will see the similarities between the area of a polygon and derive the formula for the area of a circle.

Goals

Review area of triangles, rectangles, and parallelograms.
Find the area of regular polygons.
Generalize an area formula for any regular polygon.

ELL: This lesson offers students a rich opportunity to learn academic vocabulary. Display the new terms in writing somewhere visible in the classroom so that you can refer to them. Allow ELLs to use their bilingual dictionaries to help with understanding the terms. When possible, have ELLs discuss the terms in their language of choice with other ELLs who share the same primary language.

Subject:
Geometry
Provider:
Pearson
Same Base and Height, Variation 2
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This is the second version of a task asking students to find ...

This is the second version of a task asking students to find the areas of triangles that have the same base and height. This presentation is more abstract as students are not using physical models.

Subject:
Mathematics
Geometry
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics