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Welcome to class. Please pick up and complete a pink warm up from the back table.

Welcome to class. Please pick up and complete a pink warm up from the back table. Turn in your signed progress reports for $10. Warm up. 3.1.1 – Similarity & Dilation 3.1.2 – Proportional Growth and Ratios. 3.1.1 – Dilation. Stretching is NOT dilating.

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Welcome to class. Please pick up and complete a pink warm up from the back table.

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  1. Welcome to class. Please pick up and complete a pink warm up from the back table. Turn in your signed progress reports for $10.

  2. Warm up

  3. 3.1.1 – Similarity & Dilation3.1.2 – Proportional Growth and Ratios

  4. 3.1.1 – Dilation Stretching is NOT dilating Dilation – a non-rigid transformation that changes the size of a figure while maintaining its shape. The result is a similar figure.

  5. To dilate a figure: • Start from the point of dilation • Dilate each vertex by the scale factor, making a dot at each new point. • Connect the new vertices. • Be sure to label the pre-image and image appropriately. B’ 3 This figure has a scale factor of 3. Notice that the distance between the point of dilation and the vertex can be different for each vertex. A scale factor > 1 ENLARGES the shape A scale factor < 1 REDUCES the shape 2 1

  6. Get:ONE partnerResource page 3.1.1 (one per team)scissors (one per team)straight edge (one per team)

  7. I will number you off…#1s will dilate the shape by a factor of 2#2s will dilate the shape by a factor of 3#3s will dilate the shape by a factor of 4#4s will dilate the shape by a factor of 5 1 4 3 2

  8. Distance formula Put this in your notes!! Given 2 points (x1, y1) and (x2, y2) D = √(x2 – x1)2 + (y2 – y1)2 Given 2 points (3, 4) and (0, -2) d = √(0 – 3)2 + (-2 – 4)2 d = √(-3) 2 + (-6) 2 d = √9 + 36 d = √45 d = 3√5

  9. In order for shapes to be similar, they have to be changed by the same RATIO Pre-image Notice that the image was changed by a ratio of 3 (or 3/1) from the pre-image. 2 6 Image 6 18

  10. Are these 2 shapes SIMILAR? Check the ratio of the sides: If the corresponding sides are in the same ratio, then the shapes are similar 25 17 53 34 18 36 25 = 25 53 53 17 = 1 34 2 18 = 1 36 2

  11. but... what if a side was missing a length? Then you have to set up a PROPORTION 5 17 • 5 = 3.5 • 17 x • 5 = 17 • 3.5 x or 3.5 Cross products: (notice how they are the same?) 5x = 59.9 X = 11.9 Cross products: 5x = 59.9 X = 11.9 x

  12. Your assignment Pg 138 – 143; 5-9, 17-21, not 8c

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