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Identify and describe polygons (triangles, quadrilaterals, pentagons, hexagons, etc.), using terms such as regular, convex, and concave. Find measures of angles, sides, perimeters, and areas of polygons, justifying the methods used. Apply transformations to polygons. Relate geometry to algebra by using coordinate geometry to determine transformations. Use algebraic reasoning to determine congruence, similarity, and symmetry. Create and verify tessellations of the plane using polygons.
Standard 2 : PolygonsArchived
Cluster Standards
This cluster includes the following benchmarks.
Visit the specific benchmark webpage to find related instructional resources.
- MA.912.G.2.1 : Identify and describe convex, concave, regular, and irregular polygons.
- MA.912.G.2.2 : Determine the measures of interior and exterior angles of polygons, justifying the method used.
- MA.912.G.2.3 : Use properties of congruent and similar polygons to solve mathematical or real-world problems.
- MA.912.G.2.4 : Apply transformations (translations, reflections, rotations, dilations, and scale factors) to polygons. to determine congruence, similarity, and symmetry. Know that images formed by translations, reflections, and rotations are congruent to the original shape. Create and verify tessellations of the plane using polygons.
- MA.912.G.2.5 : Explain the derivation and apply formulas for perimeter and area of polygons (triangles, quadrilaterals, pentagons, etc.).
- MA.912.G.2.6 : Use coordinate geometry to prove properties of congruent, regular and similar polygons, and to perform transformations in the plane.
- MA.912.G.2.7 : Determine how changes in dimensions affect the perimeter and area of common geometric figures.
Cluster Information
Number:
MA.912.G.2
Title:
Polygons
Type:
Standard
Subject:
X-Mathematics (former standards - 2008) - Archived
Grade:
912
Body of Knowledge
Geometry
Cluster Access Points
This cluster includes the following Access Points.
- MA.912.G.2.In.a : Determine if polygons have all sides and angles equal (regular) or have sides or angles that are not equal (irregular) using physical and visual models.
- MA.912.G.2.In.b : Use tools to measure angles including 45° and 90°.
- MA.912.G.2.In.c : Identify triangles and rectangles that are the same shape and size (congruent) and same shape, but not same size (similar) using physical and visual models.
- MA.912.G.2.In.d : Use physical and visual models to show that a change in orientation, such as turns (rotations), slides (translations), and flips (reflections), does not change the size or shape of a polygon.
- MA.912.G.2.In.e : Find the perimeter and area of rectangles to solve real-world problems.
- MA.912.G.2.In.f : Identify the effects of changes in the lengths of sides on the perimeter and area of rectangles using visual models to solve real-world problems.
- MA.912.G.2.Su.a : Identify polygons with all sides and angles equal (regular) in the environment.
- MA.912.G.2.Su.b : Use a model of a right triangle to compare the size of angles, such as acute, obtuse, and right angles.
- MA.912.G.2.Su.c : Match triangles and rectangles that are same shape, but different size (similar) using physical and visual models.
- MA.912.G.2.Su.d : Match identical polygons in different positions including turns (rotations), slides (translations), and flips (reflections), using physical models.
- MA.912.G.2.Su.e : Solve real-world problems involving perimeter using visual models.
- MA.912.G.2.Su.f : Solve real-world problems to find area of a rectangle to identify total square units using visual models.
- MA.912.G.2.Su.g : Identify the effect of changes in the lengths of sides of rectangles on perimeter using physical and visual models.
- MA.912.G.2.Pa.a : Identify objects or pictures with polygons.
- MA.912.G.2.Pa.b : Match two or more objects with polygons based on a given feature in real-world situations.
- MA.912.G.2.Pa.c : Identify objects, pictures, or signs with polygons in real-world situations.
Cluster Resources
Vetted resources educators can use to teach the concepts and skills in this topic.
Image/Photograph
- Clipart: Geometric Shapes: In this lesson, you will find clip art and various illustrations of polygons, circles, ellipses, star polygons, and inscribed shapes.
Lesson Plans
- Triangles: Finding Interior Angle Measures: The lesson begins with a hands-on activity and then an experiment with a GeoGebra-based computer model to discover the Triangle Angle Sum Theorem. The students write and solve equations to find missing angle measures in a variety of examples.
- How does scale factor affect the areas and perimeters of similar figures?: In this lesson plan, students will observe and record the linear dimensions of similar figures, and then discover how the values of area and perimeter are related to the ratio of the linear dimensions of the figures.
Video/Audio/Animation
- MIT BLOSSOMS - Using Geometry to Design Simple Machines: This video is meant to be a fun, hands-on session that gets students to think hard about how machines work. It teaches them the connection between the geometry that they study and the kinematics that engineers use -- explaining that kinematics is simply geometry in motion.