1. For example:
Jen’s bedroom is 30 feet long and 20 feet wide. Her soccer field is 120 yards long and 80 yards wide. Is Jen’s bedroom similar to her soccer field?
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2. Read

3. 20 2 20 2
You already know what ratio is, a ratio compares two quantities. In this lesson will will discuss two types of ratios, between ratios and within ratios. In this example the between ratios of the widths of the orange rectangle to the width of the green rectangle is 2 to 20, or 1 to 10. The within ratio of width to length in the orange rectangle is 2 to 6 or 1 to The between ratios of the lengths of the orange rectangle to the width of the green rectangle is 6 to 60, or 1 to 10. The within ratio of width to length in the green rectangle is 20 to 60 or 1 to 3. Notice that the orange and green rectangles have equivalent between and within ratios. In this lesson you will discover the implications of this fact.

4. Similar Shapes
Number of Sides
Same
Similar
Ratios
Between
Within
You already know what ratio is, a ratio compares two quantities. In this lesson will will discuss two types of ratios, between ratios and within ratios. In this example the between ratios of the widths of the orange rectangle to the width of the green rectangle is 2 to 20, or 1 to 10. The within ratio of width to length in the orange rectangle is 2 to 6 or 1 to The between ratios of the lengths of the orange rectangle to the width of the green rectangle is 6 to 60, or 1 to 10. The within ratio of width to length in the green rectangle is 20 to 60 or 1 to 3. Notice that the orange and green rectangles have equivalent between and within ratios. In this lesson you will discover the implications of this fact.

5. What characteristics make shapes similar?
Color
Shape
Size
Students often get confused about what similar shapes are. More specifically, students are often unsure whether similar shapes have the same or similar number of sides, between ratios, and within ratios. Similar shapes have the same number of sides, the same ratio between dimensions, and the same ratio within dimensions.

6. 120
yards
Jen’s bedroom is 30 feet long and 20 feet wide. Her soccer field is 120 yards long and 80 yards wide. Is Jen’s bedroom similar to her soccer field? To find out we are going to check the three conditions outlined in the similar shapes tree diagram.

7.
sides sides
Is the number of sides the same? Jen’s bedroom has 4 sides and the soccer field has 4 sides. Therefore, the shapes do have the same number of sides.

8. Is the ratio between the shapes the same
Is the ratio between the shapes the same? Comparing width to width we have 20 feet to 80 yards or 1 foot to 4 yards. Comparing length to length we have 30 feet to 120 yards or 1 foot to 4 yards. Which is the same ratio between shapes, but you may be wondering, don’t you have to convert the yards to feet so that you are working with the same units. Well, if we multiply the number of yards by 3, we will have the number of feet. As you can see the between ratios are still the same, they have just been multiplied by a factor of 1/3.

9. Is the ratio between the shapes the same
Is the ratio between the shapes the same? Comparing width to width we have 20 feet to 80 yards or 1 foot to 4 yards. Comparing length to length we have 30 feet to 120 yards or 1 foot to 4 yards. Which is the same ratio between shapes, but you may be wondering, don’t you have to convert the yards to feet so that you are working with the same units. Well, if we multiply the number of yards by 3, we will have the number of feet. As you can see the between ratios are still the same, they have just been multiplied by a factor of 1/3.

10. Similar Shapes
Number of Sides
Same
Similar
Between
Ratio
Within
We proved that Jen’s bedroom and the soccer field have the same number of sides, the same between ratios, and the same within ratios. Therefore, they are similar shapes.

15. Jen’s bedroom is 45 feet long and 15 feet wide
Jen’s bedroom is 45 feet long and 15 feet wide. Her soccer field is 180 yards long and 60 yards wide. Is Jen’s bedroom similar to her soccer field?