Patterns in geometry
Mathematics, Grade 8
Patterns in geometry
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Study Guide Patterns in geometry Mathematics, Grade 8
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PATTERNS IN GEOMETRY Patterns in geometry refer to shapes and their measures. • Shapes can be congruent to one another. Shapes can also be manipulated to form similar shapes. • Transformations are operations that are performed on shapes that move a shape to a different location. The types of transformations are reflection, rotation, dilation and translation. o With a reflection, a figure is reflected, or flipped, in a line so that the new figure is a mirror image on the other side of the line. o A rotation rotates, or turns, a shape to make a new figure. o A dilation shrinks or enlarges a figure. o A translation shifts a figure to a new position. • Lines of symmetry also can change a figure. Lines of symmetry break a shape into two equal mirror images. • Tessellations are patterns of regular polygons that do not overlap or have gaps. The transformations of reflection, translation, and rotation make up tessellations. How to use patterns in geometry Patterns in geometry are useful in many ways. • Congruent figures have the same size and shape. If one shape is congruent to another, all the sides and angles will be equal. For example, what is the length of side GH if the rectangles are congruent? Since the rectangles are congruent, the sides are equal, GH = 6 cm. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
• Transformations also use patterns in geometry. A reflection of a shape in a line reflects, or flips the shape so that the new figure is a mirror image of the shape on the other side of the line. For example, what does triangle A look like when it is reflected in the line y? The figure shows the reflection of triangle A in line y. The reflection is a mirror image of triangle A. • A rotation turns a figure a certain number of degrees about the origin or about a point in a figure. • A dilation is the only transformation in which the size of the new shape is different than the original shape. A dilation shrinks or enlarges a shape. If a shape is dilated with the notation, D2, that means that the new shape is double the original shape. A dilation of D.5 would mean that the new shape is one half the size of the original shape. • A translation moves or shifts a shape based on a rule. The rule applies to the x and y coordinates of the shape. For example, if a shape is translated x ,y →(x + 4, y - 2) that means that the x coordinate is increased by 4 and the y coordinate is decreased by 2. When this is done for each coordinate of a shape, a new figure is produced in a new location. • Lines of symmetry break a shape into two pieces that are mirror images. Lines of symmetry can be vertical, horizontal, diagonal or any way that breaks a shape into two mirror images. Lines of symmetry can also be used for letters or words. For example, what kind of symmetry does the letter C have? © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
The letter C has horizontal line symmetry because when a horizontal line crosses it, it is broken into two pieces that are mirror images. Rotational symmetry is when a figure is congruent to itself after being rotated 180° or less. • Tessellations are made with the transformations of reflection, rotation and transformation. The figure below is an example of a tessellation. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
Try This! 1. The two triangles shown are congruent. What is measure of the side labeled x? 2. What transformation changes a figure’s size? 3. How many lines of symmetry does a square have? 4. What are the coordinates of a triangle with the coordinates, (5, -1), (6, -1), (6, 8), after a translation of (x, y) → (x - 4, y -3)? © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
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