A scale copy of a figure is a figure that is geometrically similar to the original figure.
This means that the scale copy and the original figure have the same shape but possibly different sizes.
More precisely, the angles of the scale copy are equal to the corresponding angles of the original figure, and the ratio of the side lengths of the scale copy is the same as the ratio of the corresponding side lengths of the original figure.
In real life, a scale copy is often smaller than the original figure. For example, the drawing of a floor plan for a room is a scale copy of the actual floor of the room. The floor plan drawing has the same shape as but is smaller than the actual floor. For example, if the actual floor is a rectangle measuring 12 feet by 16 feet, a scale copy could be a drawing of a 6-inch by 8-inch rectangle (because 12ft:16ft is the same ratio as 6in:8in).
Scaled copies of each other in this diagram is bigger be a scaled version of figurehead pause a video and see if you can figure that out so there’s multiple ways if you can approach this one ways to say well let’s see what the scaling Factor so we can look at those legs side last night it was years has went three on figure a side length right over here has blank one two three four five this side lengths has length 5 is well as my own by this line you can figure it out with the Pythagorean theorem even look up the corresponding sides of that would be right over here and what is its length length when you scale it up looks like 5 so to go from 3 to 5 you would have 2 * 530 but let’s look at this time so it’s 5 in figure a what length is it in figure B what is 1 2 3 4 5 hit still fine to go from 5 to 5 you have to multiply by one if you have a different scaling factor for corresponding or what could have been corresponding side this side right over here you’re scaling up there by at all actually are not scaled version of each other let’s do another exam so in this example is bigger be a scaled version of the gray pause the video is so this side has like to decide has lengths of corresponding side or what could be the corresponding side has like six to go from 2 to 6 you have 2 X 3 if we look at these two potentially corresponding side that guy on that side once again to go from 4 to 12 you would X so that is looking good as well now to go from this side down here old version of cigarette where do the same exercise book look at the potentially corresponding sides for that side to that side to go from 4 to 12 we would * 3 then we could look at this size and desire to go from 4 what’s a good new * 32 that’s looking good so far we can look at this side and this side potentially corresponding sides once you get a room from for 12 x 3 looks good so far and then we could look at this side and decide 2.2 to 6.6 once again multiplying by 3 looking really good and then we only have one last one to check 2.2 to 6.6 once again multiplying by 3 so all of the side lengths have been scaled up by 3 so we can feel pretty good at figure B is indeed a scaled-up representation of is bigger A.
Let’s explore scaled copies.
: Printing Portraits
Here is a portrait of a student. Move the slider under each image, A–E, to see it change.
- How is each one the same as or different from the original portrait of the student?
- Some of the sliders make scaled copies of the original portrait. Which ones do you think are scaled copies? Explain your reasoning.
- What do you think “scaled copy” means?
: Scaling F
Here is an original drawing of the letter F and some other drawings.
- Identify all the drawings that are scaled copies of the original letter F drawing. Explain how you know.
- Examine all the scaled copies more closely, specifically, the lengths of each part of the letter F. How do they compare to the original? What do you notice?
- On the grid, draw a different scaled copy of the original letter F.
: Pairs of Scaled Polygons
Your teacher will give you a set of cards that have polygons drawn on a grid. Mix up the cards and place them all face up.
- Take turns with your partner to match a pair of polygons that are scaled copies of one another.
- For each match you find, explain to your partner how you know it’s a match.
- For each match your partner finds, listen carefully to their explanation, and if you disagree, explain your thinking.
- When you agree on all of the matches, check your answers with the answer key. If there are any errors, discuss why and revise your matches.
- Select one pair of polygons to examine further. Use the grid below to produce both polygons. Explain or show how you know that one polygon is a scaled copy of the other.
Are you ready for more?
Is it possible to draw a polygon that is a scaled copy of both Polygon A and Polygon B? Either draw such a polygon, or explain how you know this is impossible.
What is a scaled copy of a figure? Let’s look at some examples.
The second and third drawings are both scaled copies of the original Y.
However, here, the second and third drawings are not scaled copies of the original W.
The second drawing is spread out (wider and shorter). The third drawing is squished in (narrower, but the same height).
We will learn more about what it means for one figure to be a scaled copy of another in upcoming lessons.
Definition: Scaled Copy
A scaled copy is a copy of an figure where every length in the original figure is multiplied by the same number.
For example, triangle DEF
is a scaled copy of triangle ABC. Each side length on triangle ABC was multiplied by 1.5 to get the corresponding side length on triangle DEF
Here is a figure that looks like the letter A, along with several other figures. Which figures are scaled copies of the original A? Explain how you know.
Tyler says that Figure B is a scaled copy of Figure A because all of the peaks are half as tall.
Do you agree with Tyler? Explain your reasoning.
Here is a picture of the Rose Bowl Stadium in Pasadena, CA.
Here are some copies of the picture. Select all the pictures that are scaled copies of the original picture.
Complete each equation with a number that makes it true.
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