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Understanding Similar Shapes and Dilations in Geometry

This guide explains the concept of similar shapes through dilations in geometry. Dilations refer to the increase or decrease of a shape at a specific scale factor, resulting in shapes that maintain the same proportions but vary in size. We will explore how to create dilations by plotting points, applying a scale factor, and calculating the scale factor by comparing coordinates of original and dilated shapes. Practical exercises include plotting points and finding dilated points to reinforce understanding, making geometry interactive and engaging.

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Understanding Similar Shapes and Dilations in Geometry

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  1. Question of the day Name one two shapes that are always similar.

  2. dilations • Are the increase or decrease of a shape at a certain scale • They are always similar • Meaning same shape but different size

  3. Two things we do • We create a dilation using scale factor • Find scale factor by comparing two dialations

  4. Create dilation • First plot points given • Then multiply each coordinate by the scale factor given

  5. example • Scale factor 3 • A(1,2) B(2,4) C(3,4) • A’(1*3, 2*3) B(2*3, 4*3) C(3*3, 4*3) • Dilated shape is • A(3,6) B(6,12) C(9,12)

  6. How to find scale factor • divide two shape’s coordinates • D(1,2) E(2,3) F(4,5) • D’(3,6) E’(6,9) F’(12,15) • Divide each corresponding coordinate and get 3 • Scale factor is 3

  7. foldable • On front cover write foldable • Inside bottom glue graph paper and plot these three points • A(1,3) B(2,4) C(3,2) • On top flap • Write the points

  8. Turn to next page • On bottom cover glue graph paper • Plot same three point, connect them • On top write three points • Then figure three new dilated points using scale factor 2 • Plot those new points and connect them

  9. On last flap • Bottom flap glue graph paper • Plot these six points • D(-1,2) E(0,0) F(2,1) • D’(-2,4) E’(0,0) F’(4,2) • On top flap divide corresponding coordinates to find the scale factor

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