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Similar Figures

Similar Figures. Dr. Jason Gershman. Similar Figures. What does it mean for two triangles to be similar? What does it mean for two polygons to be similar? How do similar figures differ from congruent figures?. Triangles. An equilateral triangle has side length 10.

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Similar Figures

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  1. Similar Figures Dr. Jason Gershman

  2. Similar Figures • What does it mean for two triangles to be similar? • What does it mean for two polygons to be similar? • How do similar figures differ from congruent figures?

  3. Triangles • An equilateral triangle has side length 10. • What is the area of the triangle? • What is the perimeter of the triangle? • How will the area of the triangle and perimeter of the triangle change if the side length is 20?

  4. Regular Hexagons • Using the equilateral triangle as a guide, find the area and perimeter of a regular hexagon with side length 10. • What happens to these measure if the side length is 20?

  5. Circles • Consider two concentric circles of radii a and b • Suppose that the ratio of a:b is 1:2, find the ratio of perimeters of these two circles. Find the ratio of the areas of these two circles. • Suppose radius a > b and radius a is of length 10 units. • Find the value of b such that the ratio of areas of these circles is 1:2 • Find the value of b such that the ratio of perimeters of these circles is 1:2

  6. Rectangles and Squares • Suppose a square has diagonal of length 6. • Find the area of the square • Find the perimeter of the square • What happens to these two measures if the diagonal is doubled to length 12?

  7. Rectangles and Squares • Suppose Rectangle A has a length which is twice its width. Suppose rectangle B has the same width as rectangle A but in rectangle B, the width is twice the length. • Find the ratio of the perimeters of rectangle A: rectangle B • Find the ratio of the areas of rectangle A: rectangle B

  8. Regular Octagons • Suppose you have a regular octagon of side length 2. • Find the perimeter of this octagon • Find the area of this octagon. • Suppose you increased the length of each side to 4. Find the perimeter and area of this new octagon.

  9. Regular Polygons • Given your answers to regular polygons (triangles, squares, hexagons, octagons), make some conclusions about how the areas and perimeters of two n-gons will changes when you change the length of the side.

  10. Application- Model HO Scale • Suppose that you are making a miniature fire engine at the 1/64 scale…this means that the car will be 1/64 the length and 1/64 the width of a real car, and height 1/64 the height of a real car. • From the side, a cross section of a fire engine is a rectangle. Suppose that the length of the model is 3 inches long by 2 inches tall. Find the length and height of the real fire engine.

  11. Projection Screens • A 52 inch tv is one which is 52 inches along the diagonal. A typical 52 inch tv is 48 inches long and 20 inches tall. • Find the area of the tv • Find the perimeter of the tv • Suppose the projection is 100x the length and width of the item in the projection tube. Find the area of the figure in the projection tube.

  12. Nature • Suppose a snowflake a the shape of a regular hexagon. • John has a snowflake of side length 4 centimeters. • How many snowflakes of side length 2 centimeters will Mary need to capture to have the same area of snowflakes as John has?

  13. Similar Polygons • Think of example of similar polygons in your daily life. • Pose a problem and create a solution to it based on this lesson and an area which interests you.

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