Determining Scale Factor We are learning to…use proportional reasoning to solve for missing side lengths of polygons. Wednesday, August 19, 2015

Determining Scale Factor  Where have we seen phrase “scale factor" earlier this year? When dilating an object. A dilation is when an object is transformed by making it larger or smaller.  The object is the same shape but a different size.  This means that the original object and the dilated object are similar.  Scale Factor - The amount that the length of each side is multiplied by in order to dilate an object.

Determining Scale Factor B C A G H I 2 cm 8 cm 5 cm 20 cm 6 cm 24 cm These two triangles are similar because the ratio of corresponding sides is the same. The scale factor from the small triangle to the larger triangle is 4! x 4 To find the scale factor can you determine what factor was multiplied by a side length to create the corresponding side length? The scale of the drawing can be written as 1cm : 4 cm

Determining Scale Factor W H B R VM 10 ft 8 ft 6 ft 20 ft 16 ft 12 ft What was the scale factor used to create the smaller triangle? What type of factor creates a smaller product? x ½ The scale factor used is ½ or 0.5. The scale of the drawing can be written as 2 feet:1 foot

Determining Scale Factor  If the original shape is larger than the dilated (similar) shape then… The scale factor will be between 0 and 1.  If the original shape is smaller than the dilated (similar) shape then… The scale factor will be greater than 1.

Determining Scale Factor  How can a scale factor be helpful? If you do not know a side length you can use the scale factor to help solve for the missing length. 1. Find two corresponding sides with measurements. 2. Determine the scale factor. 3. Multiply this scale factor by the corresponding side to determine the missing side length.

Using Scale Factor to Solve for Missing Side Lengths Solve for the missing side GH. T U V F G H 10 ft 15 ft 20 ft 4 ft 3 ft Determine the scale factor… Now multiply the scale factor by the original side… If you cannot determine the scale factor divide: The scale of the drawing is:

Using Scale Factor to Solve for Missing Side Lengths Solve for the missing side RZ. K D U B R 9 m 3 m 5 m 63 m 21 m S ? Z 35 m R 13 m Determine the scale factor… Now multiply the scale factor by the original side… The scale of the drawing is:

Using Scale Factor to Solve for Missing Side Lengths T J R G B N U Q 8 m 6 m 15 m 20 m 18 m 24 m 28 m ? Determine the scale factor… Now multiply the scale factor by the original side… The scale of the drawing is: