My Object:

computer monitor (system unit)

Construction on paper

The following constructions are the front, side, and top of the computer system. The measures of the object have been dilated by the scale factor of .50 and each square unit equals half an inch.

Transformations:

The transformation that I used was dilation in order to make my figure smaller so I could copy my object. I dilated by the scale factor of 0.50.

My model: instructions

The next step I took in my hands was to tape the sides of the paper together to create a box so I could replicate the computer monitor.

My model: instructions

My Design

First, I started my construction by measuring out the copy paper and creating my rectangles.

**05.04 Honors Extension Activity**

**by: Jennifer Santos**

Measures:

Original:

16

14

7

6

5

4.5

4

2

1.75

1

Dilated Figure:

8

7

3.5

3

2

2.5

2.25

1

0.875

.50

Ratio:

The ratio of the figures is 2:1. This can be determined by looking at the measures of the original figure and the dilated figure. For example, the length of the original figure is 14 inches, while the length of the dilated figure is 7. If one was to divide the two numbers, they would find that the answer would be 2. This procedure can be done to all measures and the answer would always be 2.

measuring tape

scissors

tape

straightedge

white blank copy paper

pencil

Then I proceeded to draw the front of the computer monitor.

Finally, I cut the pieces into two separate rectangles so I could begin putting the figures together.

After this, all I did was repeat the process for each side, and the remaining sides were just the top and the side.

I taped all the sides together so the figure would be able to stand on it's own.

And of course I made sure to measure all the sides to check if they were to the ratio between the original figure and the dilated figure.

In these pictures you can see all the tape marks.

7 inches

8 inches

3.5 inches

The finished product:

Proof:

In order to determine if the figure is 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 2. This means that the ratio is always 2:1 for the two figures.

Additional Questions

1)

What object did you choose and why?

I chose to use the computer monitor because it's a good composite figure and also very easy to measure.

2)

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

I determined the appropriate measures by dilating my object to a smaller figure so my model could work around reasonable measurements

3)

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

I started by calculating all the measures of the computer monitor. Then I constructed the figure using a straight edge. I created a scale factor of 0.50 so I could make it small enough for a precise construction. Finally I constructed my model on graph paper with pencil. After this I grabbed a couple of white sheets of copy paper and measured the right lengths since I was using a scale factor. I cut out the pieces and then proceeded to tape all the sides together so my model could stand. I measured the pieces one final time to make sure they were right and then took pictures.

4)

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

The thing that challenged me the most was making this entire prezi presentation, and also choosing what figure I wanted to replicate.

5)

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

Since my figure was basically a rectangular prism, i referred to the definition of a rectangle a lot and also the properties of congruent figures as well as the properties of similar figures.

6)

What did you think of this activity?

In my opinion, this activity was very time consuming but it was cool to see that I created an exact replica of my computer monitor.