# Projecting and Scaling

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Finding the Sides Lengths of Rectangles that are Scaled Copies.

Rectangles were made by cutting an 8 1/2-inch by 11-inch piece of paper in half, in half again, and so on, as illustrated in the diagram. The full sheet of paper is rectangle A. Find the lengths of each rectangle and enter them in the appropriate table.

Some of the rectangles are scaled copies of the full sheet of paper (Rectangle A). Record the measurements of those rectangles in this table. Rectangle A is not drawn to scale.

Some of the rectangles are NOT scaled copies of the full sheet of paper (Rectangle A). Record the measurements of those rectangles in this table.

(1). Look at the measurements for the rectangles that are scaled copies of the full sheet of paper. What do you notice about the measurements of these rectangles?

(2). Look at the measurements for the rectangles that are not scaled copies of the full sheet. What do you notice about these measurements?

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Does Equal Division of Side Lengths of a Rectangle Result to Scaled Copies?

The rectangles that are stacked together are scaled copies of the full sheet so that they all line up at a corner, as shown in the diagram.

(1). On each stack, draw a line from the bottom left corner to the top right corner of the biggest rectangle. What do you notice?

(2). In many countries, the standard paper size is not 8.5 inches by 11 inches (called “letter” size), but instead 210 millimeters by 297 millimeters (called “A4” size).  Are these two rectangle sizes scaled copies of one another?

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Solving Problems on Dilation.

Draw a scaled copy of Polygon A with scale factor .

Draw a scaled copy of Polygon C with scale factor .

Draw a scaled copy of Polygon B with scale factor 2.

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Rectangle A has length 12 and width 8. Rectangle B has length 15 and width 10. Rectangle C has length 30 and width 15.

(1). Is Rectangle  A  a scaled copy of Rectangle  B? If so, what is the scale factor?

(2). Is Rectangle  B  a scaled copy of Rectangle  A? If so, what is the scale factor?

(3). Explain how you know that Rectangle  C  a scaled copy of Rectangle  B.

(4). Is Rectangle  A  a scaled copy of Rectangle  C? If so, what is the scale factor?

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Here is a picture of Rectangle R, which has been evenly divided into smaller rectangles. Two of the smaller rectangles are labeled B and C.

(2). Is C  a scaled copy of B? If so, what is the scale factor?

(3). Is C a scaled copy of R? If so, what is the scale factor?

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Rectangle A  measures 12 cm by 3 cm. Rectangle B  is a scaled copy of Rectangle A. Select all of the measurement pairs that could be the dimensions of Rectangle B.