Biggie Size It!

Name ___________________________________________________Date___________

Open the file Double in GSP.

You should see two triangles. Each side of the second triangleis twice as long as the side it corresponds to in the first triangle.You can change the shape of the triangle (by dragging points around),but the length of the sides of one triangle will always be twiceas long as the sides in the other triangle. Observe the differentmeasurements on your screen and answer the questions below.

1. How many times bigger is the perimeter of triangle ADE than the perimeter of triangle ABC? _______________

2. What is the ratio of the perimeters of triangle DEF to triangle ABC? ______________

3. How many times larger is the area of triangle DEF than the area of triangle ABC? _____________

4. What is the ratio of the areas of triangle DEF to triangle ABC? _____________

5. Does the ratio of the perimeters and areas change as the shape and size of the two triangles changes? (If yes, give example) _______________________________

6. Write a sentence or two summarizing what you have observed. __________________________________________________________________

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Now, let's look at why this is true.

1. Write a formula to find the perimeter of the original triangle in terms of the sides "j," "k," and "l." P = _________________________

 

2. Since we know that sides a, b, and c are twice as long in the second triangle, how could you write a formula to find the perimeter of the second triangle in terms of sides j, k, and l? P = ________________________________

 

3. Explain why the perimeter will always equal twice as much if you double the length of the sides.

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Now, let's look at the area.

1. What is the formula to find the area of any triangle? A = ________________

 

2. How many times larger will the base of the larger triangle be? ____________

 

3. Click on the "Show height" button. How many times larger is the height of the

larger triangle ? ____________

 

4. Explain why the area will always be four times greater if you double the length of the sides on a

 

triangle. ___________________________________________________________

 

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Open the file Triple in GSP. In this file, the lengthof the sides of the larger triangle are three times as much asthe smaller triangle. Drag the vertices of the triangle aroundand observe what is happening to the measurements.

1. Compare the ratio of the perimeters of these two triangles. _______________________

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Use the formula for finding perimeter to explain why this is true.

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2. Compare the ratio of the areas of the two figures. ______________________________


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Use the formula for area of triangles to explain why this is true. (Click on "Show Heights" button to see the ratio of the two heights). _______________________________________________________________________

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3. Based on this information, What would you expect to happen to the perimeter if we made the sides of

 

the second triangle four times larger? ___________________________________. What about the area?

 

_____________________ If we made the sides of the triangle ten times larger, what would happen to the area and perimeter?

 

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Explain why you think this will happen. ________________________________________


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