**4.05 Module Four Activity**

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Reflection Questions

In the example floor plan of a bedroom above, the bed measures 5.5 squares x 8 squares. When the actual dimensions of the bed are found, the bed is approximately 55 in. x 80 in. which converts to approximately 4.5 ft. x 6.6 ft. After creating your floor plan and using your scale factor to find the actual dimensions of the objects placed in the room, do you think the sizes are true-to-life and represent real-world sizes? Explain your answer using complete sentences and provide details in your writing.

Using your floor plan, select three items in the room to connect together to create a triangle. The example below shows the bedroom floor plan shown earlier with a triangle connecting the bed, dresser, and desk. Imagine this floor plan was brought to life in the actual apartment complex and each piece of furniture was placed exactly as shown below. If the real-life objects were connected by string to mimic the triangle below, what would you know about the triangle created on the floor plan and the triangle created in the actual room? What information could you state as fact regarding corresponding sides and corresponding angles? Are the two triangles similar? Explain your answer using complete sentences and provide details in your writing.

The winning designs will be chosen to place on a brochure for the apartment complex. The space given on the brochure for your room is 3 in. x 4 in. Explain how you would use the triangle you created for part 1 to reduce the size of your design so it would fit in the space provided on the brochure. Use complete sentences and provide details in your writing.

How could you use the Angle-Angle postulate to prove that the triangle on your floor plan is similar to the triangle in the real-life room? Use complete sentences and provide details in your writing.

In this section, please write a short descriptive paragraph of the room that you have chosen and the process you will go through in converting your scaled measurements to the actual dimensions.

**By: Destyn Phillips & Jordan Phillips**

We have chosen a bedroom that has a bed, a nightstand, a desk, and a dresser. The scale is two inches to two feet, this is pretty accurate because the size of my bed is seventy-two inches and once you convert it, that becomes the size of the scaled down bed. We will convert the measurements by using the scale factor 1/12. You figure out the scale factor by: 2 in/2 ft * 1 ft/12 in= 2/24, which is 1/12.

2 Inches= 2 feet

Key:

6 in.

4 in.

3.5 in.

1.5 in.

1 in.

2 in.

1.5 in.

2.5 in.

Bed

1/12

Desk

Night Stand

Dresser

6" x 3"

6'x 3'

3.5"x1.5"

3' 1/2"x1' 1/2"

2"x1"

2'x1'

2 1/2"x1 1/2:

2'.5"x1'.5"

Yes, These dimensions are real-world sizes.

These sizes are normal sizes for the average human.

My own bedding happens to be roughly around this size frame. And I can sleep cozy upon it.

The two triangles would be similar in real life and on the drawing. They would have corresponding sides, and angles. The triangles mimic each other by shape and size, one just happens to be bigger than the other, therefore making them similar. The two triangles would look alike one another on and off the paper.

I would reduce the size by 1/6 (this would be the scale factor) because that would make the triangle fit into the 3 in x 4 in space. This would provide enough room because the triangle was 18 in. x 24 in., and if you reduced it by 1/6, it would make it exactly 3 in. x 4 in.

By using Angle-Angle postulate, you could very easily prove that the triangles are similar because, when you actually figure out the first and second angle, it is very simple to compare the two and see that they are similar. Angle-Angle postulate means: If two corresponding angles of two or more triangles are congruent, the triangles are similar. So, that would make sure that they are similar triangles.

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