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Understanding Similar Figures: Sides, Areas, and Volumes

Learn about the concept of similar figures, how their sides, areas, and volumes are related, and how scaling factors influence these properties.

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Understanding Similar Figures: Sides, Areas, and Volumes

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  1. Example 1 Example 2 Similar Figures Definition: Figures are similar if they have the same shape but not necessarily the same size. Triangles are similar if they have the same angles.

  2. bk b Scale by k ak a Scale Factors The Sides of similar figures are related by a Scale Factor

  3. Similar Triangles Similar Triangles have the same angles x b a y z Their sides are connected by the scale factor: a=kp b=kq c=kr c Scale factor k x p q y z r

  4. Scale by k bk b ak a Areas of Similar Figures Area = ab Area = ak x bk = abk2 If sides scale by k then Area scales by k2

  5. c ck b bk a ak Scale by k Volume of Similar Figures Volume = abc Volume = ak x bk x ck = abck3 If the sides scale by k then the Volume will scale by k3

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