# 5.14 - Transformations and Polygons

The student will

a)  recognize and apply transformations, such as translation, reflection, and rotation; and

b)  investigate and describe the results of combining and subdividing polygons.

### BIG IDEAS

• So that I can recognize the movement of shapes within a geometric pattern
• So that I can create pictures using Tangrams
• So that fashion designers can design fun printed fabrics for clothing
• So that artists can subdivide shapes when creating their masterpieces

### UNDERSTANDING THE STANDARD

• A transformation of a figure (preimage) changes the size, shape, or position of the figure to a new figure (image). Transformations can be explored using mirrors, paper folding, and tracing.
• Congruent figures have the same size and shape.
• A translation is a transformation in which an image is formed by moving every point on the preimage the same distance in the same direction.
• A reflection is a transformation in which an image is formed by reflecting the preimage over a line called the line of reflection.  All corresponding points in the image and preimage are equidistant from the line of reflection.
• A rotation is a transformation in which an image is formed by rotating the preimage about a point called the center of rotation. The center of rotation may or may not be on the preimage.
• The resulting figure of a translation, reflection, or rotation is congruent to the original figure.
• The orientation of figures does not affect congruency or noncongruency.
• A polygon is a closed plane figure composed of at least three line segments that do not cross.
• Two or more polygons can be combined to form a new polygon. Students should be able to identify the figures that have been combined.
• A polygon that can be divided into more than one basic figure is said to be a composite figure (or shape).  Students should understand how to divide a polygon into familiar figures using concrete materials (e.g., pattern blocks, tangrams, geoboards, grid paper, paper (folding), etc.).

• This diagonal of the rectangle above subdivides the rectangle in half and creates two right triangles.  The figure can also be formed by combining two right triangles that are congruent.  The resulting figure shows that the legs of the right triangles are congruent to the sides of the rectangle.  The representation illustrates that the area of each right triangle is half the area of the rectangle.  Exploring decomposition of shapes helps students develop algorithms for determining area of various shapes (e.g., area of a triangle is ½ × base × height).
• Congruent sides are denoted with the same number of hatch (or hash) marks on each congruent side. For example, a side on a polygon with two hatch marks is congruent to the side with two hatch marks on a congruent polygon or within the same polygon.

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections and representation to

• Apply transformations to polygons in order to determine congruence. (a)
• Recognize that translations, reflections, and rotations preserve congruency. (a)
• Identify the image of a polygon resulting from a single transformation (translation, reflection, or rotation). (a)
• Investigate and describe the results of combining and subdividing polygons. (b)
• Compare and contrast the characteristics of a given polygon that has been subdivided with the characteristics of the resulting parts. (b)

### KEY VOCABULARY

Updated: Aug 22, 2018