University:
Bradley University
Course:
MTH 119 | Calculus With Review B
Academic year:

2019
Views:

207

Pages:

2
Author:

Shyanne Johnson

Reading Guide Similarity  What are the two informal definitions of similar shapes, according to the textbook? Two objects that have the same shape, but not the same size. Two objects or shapes are similar if one object represents a scaled version of the other (scaled up or down).  How to create a shape or design that is similar to another shape or design by using grids of lines? Draw a grid of equally spaced parallel and perpendicular lines over the design you want to scale, if you want the new design to be twice as wide and twice as long, then make a new grid of parallel and perpendicular lines that are spaced twice as wide as the original. Now copy the design on the new grid, the design will be similar to the original.  Explain why the designs in figure 14.59 are similar. The designs are similar because both graphs show the face of a rabbit and the points are the same, only one is wider than the other. The new graph is spaced equally parallel and perpendicular.  Explain why the designs in figure 14.60 are not similar. The width as a different relationship to the original than the height does. The middle one is the same height as the original but half as wide. The right design is as wide as the original but half as tall.  What is the formal definition of similar shapes? Two shapes or objects (in a plane or space) are similar if every point on one object corresponds to a point on the other object and there is a positive number (Say k) of distance between any two points on the second object is k times long as the distance between the corresponding points on the first object.  What does “scale factor” mean? A collection of distances within the second object (length, width, height) are in the same ratio as the corresponding distances within the first object.  Read carefully to understand how to solve the sculpture problems using the “scale factor method” and the “internal factor method”. Scale factor method: every length on the actual sculpture is k times as long as the corresponding length on the scale model. Internal factor method: If the scale model is 5 inches wide by 10 inches tall, it is 10/5 = 2 times as tall and wide.  What does “scale factor” mean? Give an example. Every length on the actual sculpture is k times as long as the corresponding length on the scale model. 20/10=x/60 sculpture height:60*20=120 inches  What does “internal factor” mean? Give an example. As the scale model is 10 inches wide and 20 inches tall, it is 20/10=2 times as tall as it is wide. The actual sculpture should therefore also be 2 times as tall as it is wide. 2*60=120 inches.  What does it mean to say that with the “scale factor method” we compare like quantities? It means we can think of it as an external comparison method because it compares like parts across two different shapes. Reading Guide  What does it mean to say that with the “internal factor method” we compare unlike quantities? We can think of it as an internal comparison method because it compares different parts within one shape.