**05.04 Honors Extension**

Measures:

Original:

44

22

48

32

8

8

I started my construction by measuring out the cardboard and marking the points I had to cut off. I then cut the cardboard so that I could begin putting the figure together.

After taping the pieces of cardboard together to replicate the front of the dresser, I used my pen and measuring tape to mark the points of the dressers drawers. I went over the marks with a permanent marker to make them easier to see.

I connected the points using a permanent marker as well as a straightedge to make sure the lines were straight. I then taped on the other pieces of cardboard I needed to make my figure three-dimensional. Finally, I measured the figure one last time to make sure the dimensions wer correct.

Proof:

My Object:

The Finished Product

Materials:

Dresser

Pen

Permanent Marker

Cardboard

Straightedge

Measuring Tape

Tape

Scissors

Construction on Paper:

The following constructions are those of the front and side of the dresser. The measures of the object have been dilated by the scale factor of .25. Each square unit is equal to an inch.

Dilated Figure:

11

5.5

12

8

2

2

Transformations:

In order to have the ability to replicate my object, I had to dilate it to make it smaller. I dilated it by the scale factor of .25.

Ratio:

The ratio of the figures is 4:1. This can be determined by looking at the relationship between the measures of the original figure and the dilated figure. In example, the width of the original figure is 44 inches, while the width of the dilated figure is 11. If one was to divide the two numbers, they would find that the answer would be 4. This procedure can be done for all of the measures and the answer would always be 4.

In order to determine if the figures are similar, each pair of corresponding sides must have the same ratio. As demonstrated beforehand, when taking any two corresponding measures of the figure and dividing them by one another, one would find that the answer is always 4. This means that the ratio is always 4:1 for the two figures.

Additional Questions:

What object did you choose to make a model of and why?

I chose the dresser in my living room because it is a composite figure and it was a good size to record the exact measures of.

How did you determine the appropriate dimensions between the object and its model?

I made sure the figure was small enough to be able to calculate the exact measures. I also dilated the image so that I could work with smaller numbers.

What steps did you take to create your model? Be sure to include all mathematical calculations.

I started by calculating all of the measures of the dresser. I then constructed the figure using a straightedge. To make it small enough for an accurate construction, I dilated it by the scale factor of .25. Then, I started constructing my figure. I measured pieces of cardboard, cut them out, taped them together, and measured one final time to be sure that the figure's measures were correct.

What challenges, if any, did you experience during this process?

The most challenging part for me was determining which figure I was going to replicate because I had to make sure that it would not be too large to create.

What geometric principles, properties, postulates, or theorems did you use to make your model?

I used the definition of a rectangle as a reference while creating the figure. I also looked at the properties of similar figures.

What did you think of this activity?

I thought it was challenging, which I liked. It was also really cool to be able to replicate a figure on my own.