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Standard 2 : Polygons (Archived) This document was generated on CPALMS - www.cpalms.org 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. Number: MA.912.G.2 Title: Polygons Type: Standard Subject: X-Mathematics (former standards - 2008) - Archived Grade: 912 Body of Knowledge: Geometry Related Benchmarks Code Description Identify and describe convex, concave, regular, and irregular polygons. Remarks/Examples: MA.912.G.2.1: Example 1: Draw a hexagon. Is it convex or concave? Is it regular or irregular? Explain your answers. Example 2: Define the terms convex, concave, regular and irregular polygon and draw a picture of the tern next to the definition. Determine the measures of interior and exterior angles of polygons, justifying the method used. MA.912.G.2.2: Remarks/Examples: Example 1: Calculate the measure of one interior angle and one exterior of a regular octagon. Explain your method. Example 2: Suppose that you will make a picture frame like the one shown below. To make the regular hexagonal frame, you will use identical trapezoidal pieces. What are the measures of the angles of the trapezoids? Explain your answer. Use properties of congruent and similar polygons to solve mathematical or real-world problems. Remarks/Examples: Example: Suppose a building is in the shape of a regular hexagon. The architect wants to put walkways as indicated. Show that the triangles formed are equal in size and shape. MA.912.G.2.3: 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. Remarks/Examples: MA.912.G.2.4: Physical objects, drawings, and dynamic geometry software might help students explore this benchmark. Students' early work in elementary and middle school should form a base for teaching this benchmark (see MA.3.G.3.3, MA.4.G.5.2, and MA.7.G.4.2). Students should explore different types of transformations and observe that some transformations (translations, reflections, and rotations) result in congruent shapes. Example: Explore regular polygons through manipulatives and/or drawing programs. Describe which of the polygons would be best for tiling a rectangular floor. Explain your reasoning. Explain the derivation and apply formulas for perimeter and area of polygons (triangles, quadrilaterals, pentagons, etc.). Remarks/Examples: Example 1: A rectangle of area 360 square yards is ten times as long as it is wide. Find its length and width. Example 2: Explain the derivation of the formula for the area of a triangle. MA.912.G.2.5: Example 3: The design below is called the Ohio Star. Assuming that it measures 9 inches by 9 inches, calculate the total area of all the orange patches, the total area of all the yellow patches, and the total area of all the green patches. How much fabric of each color will you need to cover an area that measures 72 inches by 90 inches? Use coordinate geometry to prove properties of congruent, regular and similar polygons, and to perform transformations in the plane. Remarks/Examples: MA.912.G.2.6: Example: Draw the polygon defined by the following vertices ( 1, 3), ( -1, 3), (3, 1), (-3, 1), (1, -3), (-1, -3), (-3, 1), (3, -1). Is this polygon regular? Justify your answer. Example: Is the polygon formed by connecting the points (2, 1), ( 6, 2), (5, 6), and (1, 5) a square? Justify your answer. Determine how changes in dimensions affect the perimeter and area of common geometric figures. MA.912.G.2.7: Remarks/Examples: Example: If the lengths of each side of a trapezoid are tripled, determine the change in its area, and justify your answer. Related Access Points Independent Access Point Number MA.912.G.2.In.a: MA.912.G.2.In.b: MA.912.G.2.In.c: MA.912.G.2.In.d: MA.912.G.2.In.e: MA.912.G.2.In.f: Access Point Title 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. Use tools to measure angles including 45° and 90°. 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. 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. Find the perimeter and area of rectangles to solve real-world problems. 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. Supported Access Point Number MA.912.G.2.Su.a: MA.912.G.2.Su.b: MA.912.G.2.Su.c: MA.912.G.2.Su.d: MA.912.G.2.Su.e: MA.912.G.2.Su.f: MA.912.G.2.Su.g: Access Point Title Identify polygons with all sides and angles equal (regular) in the environment. Use a model of a right triangle to compare the size of angles, such as acute, obtuse, and right angles. Match triangles and rectangles that are same shape, but different size (similar) using physical and visual models. Match identical polygons in different positions including turns (rotations), slides (translations), and flips (reflections), using physical models. Solve real-world problems involving perimeter using visual models. Solve real-world problems to find area of a rectangle to identify total square units using visual models. Identify the effect of changes in the lengths of sides of rectangles on perimeter using physical and visual models. Participatory Access Point Number MA.912.G.2.Pa.a: MA.912.G.2.Pa.b: MA.912.G.2.Pa.c: Access Point Title Identify objects or pictures with polygons. Match two or more objects with polygons based on a given feature in real-world situations. Identify objects, pictures, or signs with polygons in real-world situations. Related Resources Image/Photograph Name Clipart: Geometric Shapes: Description In this lesson, you will find clip art and various illustrations of polygons, circles, ellipses, star polygons, and inscribed shapes. Lesson Plan Name Description This lesson introduces students to Rep-tiles, geometric figures which can be copied and can be fit together to make a larger Covering the Plane with Rep-Tiles: figure of the same shape. Visualizing and performing these transformations with the shapes involved encourages the student's spatial sense. In this lesson plan, students will observe and record the linear dimensions of similar How does scale factor affect the areas and perimeters of similar figures?: figures, and then discover how the values of area and perimeter are related to the ratio of the Triangles: Finding Interior Angle Measures: linear dimensions of the figures. In this lesson plan, students will start with a hands-on activity and then experiment with a GeoGebra-based computer model to investigate and discover the Triangle Angle Sum Theorem. Then they will use the Triangle Angle Sum Theorem to write and solve equations and find missing angle measures in a variety of examples. Video/Audio/Animation Name Description 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 MIT BLOSSOMS - Using Geometry to Design Simple Machines: between the geometry that they study and the kinematics that engineers use -- explaining that kinematics is simply geometry in motion. Virtual Manipulative Name Transformations - Dilation: Student Resources Description Students use a slider to explore dilation and scale factor. Students can create and dilate their own figures. (source: NLVM grade 6-8 "Transformations - Dilation") Title Transformations - Dilation: Description Students use a slider to explore dilation and scale factor. Students can create and dilate their own figures. (source: NLVM grade 6-8 "Transformations - Dilation") Parent Resources Title Clipart: Geometric Shapes: Transformations - Dilation: Description In this lesson, you will find clip art and various illustrations of polygons, circles, ellipses, star polygons, and inscribed shapes. Students use a slider to explore dilation and scale factor. Students can create and dilate their own figures. (source: NLVM grade 6-8 "Transformations - Dilation")