4.2 What Do These Shapes Have In Common? Pg. 7 Similarity

4.3 – What Do These Shapes Have In Common? Similarity This year you organized shapes into groups based on their size, angles, sides, and other characteristics. You identified shapes using their characteristics and investigated relationships between different kinds of shapes, so that now you can tell if two shapes are both parallelograms or trapezoids, for example. But what makes two figures look alike?

Today you will be introduced to a new transformation that enlarges a figure while maintaining its shape, called a dilation. After creating new enlarged shapes, you and your team will explore the interesting relationships that exist between figures that have the same shape.

4.11 – WARM-UP STRETCH Before computers and copy machines existed, it sometimes took hours to enlarge documents or to shrink text on items such as jewelry. A pantograph device (like the one at right) was often used to duplicate written documents and artistic drawings. You will now employ the same geometric principles by using rubber bands to draw enlarged copies of a design. Your teacher will show you how to do this.

Corresponding angles are equal Corresponding sides are bigger a. What do you notice about the angles of the original and the dilation? b. What do you notice about the sides of the original and the dilation?

4.12 – DILATION In problem 4.11, you created designs that were similar, meaning that they have the same shape. But how can you determine if two figures are similar? What do similar shapes have in common? To find out, your team will need to create similar shapes that you can measure and compare.

Resource Manager: Only one that can ask teacher a question (does 2x) Facilitator: Checks to make sure everyone understands, takes turns reading (does 3x) Recorder/Reporter: Makes sure everyone knows how to draw (does 4x) Team Captain: Keeps group on task, fills in for missing students, keeps track of time (does 5x)

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b. Carefully cut out your enlarged shape and compare it to your teammates' shapes. How are the four shapes different? How are they the same? As you investigate, make sure you record what qualities make the shapes different and what qualities make the shapes the same. Then complete the conditional statement.

If a shape is similar, then its ________ are congruent and its sides are ______________, angles proportional

4.13 – ZOOM FACTOR AND SCALE FACTOR In the previous problem, you learned that you can create similar shapes by multiplying each side length by the same number. This number is called the zoom factor or the scale factor. You may have used a zoom factor when using a copy machine. For example, if you set the zoom factor on a copier to 50%, the machine shrinks the image in half (that is, multiplies by 0.5) but keeps the shape the same. In this course, the zoom factor and the scale factor will be used to describe the ratio of the new figure to the original.

15 5 What zoom factor was used to enlarge the puppy shown at right? = 3

4.14 – CASEY'S "C" Casey decided to enlarge her favorite letter: C, of course! Your team is going to help her out. Have each member of your team choose a different zoom factor below. Then on the grid, enlarge (or reduce) the block "C" below by your zoom factor.

Resource Manager: Only one that can ask teacher a question (does 3x) Facilitator: Checks to make sure everyone understands, takes turns reading (does 2x) Recorder: Makes sure everyone knows how to draw (does 1x) Team Captain: Keeps group on task, fills in for missing students, keeps track of time (does 1/2x)

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x

1x

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4.15 – MULTIPLY VS. ADD Can you create a similar shape if you add the same number to each side? Examine this again with the rectangle at right. Multiply each side by 3. Then add 3 to each side of the rectangle. When does this shape appear to be similar to the original?

x3

Rectangles are only similar when multiplied, not added 4.15 – MULTIPLY VS. ADD Can you create a similar shape if you add the same number to each side? Examine this again with the rectangle at right. Multiply each side by 3. Then add 3 to each side of the rectangle. When does this shape appear to be similar to the original?

4.16 – SYMBOLS Talk about the differences of each of the symbols below. What do you think each one is written the way it is? How are they alike? How are they different? a.Equal to (=)b. Approximately c. Similar (~)d. Congruent Exactly the same Close Estimate Alike, but not equal Equal, but not exactly the same

4.17 – PICTURES Draw an example of a shape that is similar and congruent to the following.

4.18 – CONGRUENT VS. EQUAL When you are talking about numbers that are the same, we can say they are equal. However, when it is a shape, we call it congruent, because it isn't exactly the same. Use this idea to complete the statements below.