Lesson 1: Determining Similarity - Basic Problems

   Constructing Knowledge

Problem solving in this chapter is similar to what you have encountered in previous units. Labelled diagrams will help keep your work organized as will having a "plan of attack".

   Multimedia

A video describing Example 1 is provided.



EXAMPLE 1

Sawyer works in a photography shop. A customer asked if the 5 inch by 7 inch photograph of the wolf could be turned into a poster that is 18 inches by 24 inches. The customer would prefer if the photo is not altered. Is this possible?

Solution


For the picture to not be altered, the poster would need to be similar to the original picture. This means the corresponding side length ratios would need to be the same. Because both shapes are rectangles, all corners are 90° so all of the angle measures are congruent.

Step 1: Draw and label a diagram. In this case the diagram would involve both the original photo and the proposed poster.


Step 2: Determine if the rectangles are similar by comparing corresponding side length ratios.

Relative position side length ratio poster : picture
\(\frac{\text{poster width}}{\text{picture width}}=\frac{\text{FH}}{\text{AC}}=\frac{24}{7}\)

ratio = 3.428
\(\frac{\text{poster length}}{\text{picture length}}=\frac{\text{HI}}{\text{CD}}=\frac{18}{5}\)

ratio = 3.6

The corresponding side length ratios are not exactly the same, therefore the photo can not be enlarged without altering either the size of the poster or the dimensions of the original photo (by cropping it slightly).

   Points to Ponder

In this example, just because the photo does not "fit" exactly does not mean the poster could not be made. Often, photographs do need to be cropped to slightly different shapes. Fortunately, photograph software programs do the math for us and show the cropping lines for the various standard sizes.


Now, it is your turn! Complete the questions in your Chapter 8, Lesson 1 Practice Makes Perfect that refer to Basic Problems.



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