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7  - similar figures
 

7 - similar figures

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    7  - similar figures 7 - similar figures Presentation Transcript

    • Similar Figures(Not exactly the same, but pretty close!)
    • Let’s do a little review workbefore discussing similar figures.
    • Congruent Figures• In order to be congruent, two figures must be the same size and same shape. ≅
    • Similar Figures• Similar figures must be the same shape, but their sizes may be different. ≅
    • Similar Figures ≅ This is the symbol that means “similar.”These figures are the same shape but different sizes. ≅
    • SIZES• Although the size of the two shapes can be different, the sizes of the two shapes4must differ by a factor. 2 6 6 3 1 3 ≅ 2
    • SIZES• In this case, the factor is x 2. 4 2 3 3 ≅ 6 6 1 2
    • SIZES• Or you can think of the factor as 2. 4 2 3 3 ≅ 6 6 1 2
    • Enlargements• When you have a photograph enlarged, you make a similar photograph. ≅ X3
    • Reductions• A photograph can also be shrunk to produce a slide. 4 ≅
    • Determine the length of the unknown side. 1512 ≅ 4 ? 3 9
    • These triangles differ by a factor of 3. 15 3= 5 1512 ≅ 4 ? 3 9
    • Determine the length of the unknown side. ? 24 ≅ 24
    • These dodecagons differ by a factor of 6. ? = 12 2 x6 24 ≅ 24
    • Sometimes the factor between 2 figures is not obvious and some calculations are necessary.12 15 ≅ 8 10 18 12 ?=
    • To find this missing factor, divide 18 by 12.12 15 ≅ 8 10 18 12 ?=
    • 18 divided by 12 = 1.5
    • The value of the missing factor is 1.5.12 15 ≅ 8 10 18 12 1.5 =
    • When changing the size of a figure, will the angles of the figure also change? ? 4070 70 ? ?
    • Nope! Remember, the sum of all 3angles in a triangle MUST add to 180 degrees. If the size of the angles were 40 increased, 40 the sum would exceed 180 degrees.70 70 70 70
    • We can verify this fact by placing the smaller triangle inside the larger triangle. 40 4070 70 70 70
    • The 40 degree anglesare congruent. 40 70 70 70 70
    • The 70 degree anglesare congruent. 40 40 70 70 70 70
    • The other 70 degreeangles are congruent. 4 40 70 7070 70 70
    • Find the length of the missing side. 50 30 ? 6 40 8
    • This looks messy. Let’stranslate the two triangles. 50 30 ?6 40 8
    • Now “things” are easier to see. 50 30 ?6 40 8
    • The common factor betweenthese triangles is 5. 50 30 ?6 40 8
    • So the length ofthe missing side is…?
    • That’s right! It’s ten! 50 30 106 40 8
    • Similarity is used to answer real life questions. • Suppose that you wanted to find the height of this tree.
    • Unfortunately all that you have is a tapemeasure, and you aretoo short to reach the top of the tree.
    • You can measure the length of the tree’s shadow. 10 feet
    • Then, measure the length of your shadow. 10 feet 2 feet
    • If you know how tall you are,then you can determine how tall the tree is. 6 ft 10 feet 2 feet
    • The tree must be 30 ft tall. Boy, that’s a tall tree! 6 ft 10 feet 2 feet
    • Similar figures “work” just like equivalent fractions. 30 5 66 11
    • These numerators anddenominators differ by a factor of 6. 30 6 5 6 66 11
    • Two equivalent fractions are called a proportion.30 566 11
    • Similar Figures• So, similar figures are two figures that are the same shape and whose sides are proportional.
    • Practice Time!
    • 1) Determine the missing side of the triangle. ? 5 93  4 12
    • 1) Determine the missing side of the triangle. 15 5 93  4 12
    • 2) Determine the missing side of the triangle.6 6 36 36  4 ?
    • 2) Determine the missing side of the triangle.6 6 36 36  4 24
    • 3) Determine the missing sides of the triangle. 39 ? 33  ? 824
    • 3) Determine the missing sides of the triangle. 39 13 33  11 824
    • 4) Determine the height of the lighthouse.8  ? 2.5 10
    • 4) Determine the height of the lighthouse.8  32 2.5 10
    • 5) Determine the height of the car. ?3  5 12
    • 5) Determine the height of the car. 7.23  5 12
    • THE END!