Warm up: Graph (2,3) Draw in a slope triangle from (0,0) Draw a slope triangle that is twice as big. Draw a slope triangle that is 3 times as big.

2.2.1 Dilations September 12, 2018 HW: 2-51 through 2-56

CO: SWBAT dilate images. Objectives CO: SWBAT dilate images. LO: SWBAT investigate the characteristics that the image shares with the original.

What is the relationship between the image and the original? This is a type of transformation, called a “dilation”, and the figure drawn using the rubber band chain is an image of the original figure. When a figure is dilated, it is stretched proportionally from a stretch point.  The result is an enlarged or reduced figure that looks the same as the original figure.  The stretch point is called the “point of dilation” or the “center of dilation”. What is the relationship between the image and the original? Create “What if… ?” questions that can spur further investigation.  Such as… What happens if the point of dilation is closer to the original figure?  What if it is moved farther away?  What if the point of dilation is inside of the figure? What would change if we used four rubber bands?  Or five? How can we change the orientation of the image?

When an image is dilated, the angles are congruent and the sides are 2-47.  Stretching a figure as you did in problem 2-46 is a transformation called a dilation.  What does a dilated image have in common with the original figure?  To answer this question, your team will create dilations that you can measure and compare. Locate the polygon shown in Diagram #1. Imagine that a rubber band chain is stretched from the origin so that the first knot traces the perimeter of the original polygon.  Dilate the polygon from the origin by imagining a chain of 2(#1), 3(#2), 4(#3), or 5(#4) rubber bands to form A'B'C'D'. Carefully trace your dilated polygon from Diagram #1 on tracing paper and compare it to your teammates’ polygons.  How are the four dilation images different?  How are they the same?  As you investigate, make sure you compare both the angle measures and the side lengths of the polygons. When an image is dilated, the angles are congruent and the sides are proportional (100 dilations = 100 times the side length)

2-47.  Stretching a figure as you did in problem 2-46 is a transformation called a dilation.  What does a dilated image have in common with the original figure?  To answer this question, your team will create dilations that you can measure and compare. Locate the polygon shown in Diagram #1. Locate Diagram #2 on the resource page.  Dilate it by a factor of 3 (with three rubber bands) using point D as the center of dilation.  Do your observations from part (b) still apply?  What conjectures can you make about dilating any polygon?  Be prepared to share your ideas with the class.

2-49. Examine the triangles. They are drawn to scale. Are they similar?  Justify your answer.  Use tracing paper to help. Which of the following statements are correctly written and which are not?  Note that more than one statement may be correct.  Discuss your answers with your team. ΔDOG ~ ΔCAT ΔDOG ~ ΔCTA ΔOGD ~ ΔATC ΔDGO ~ΔCAT 16 8 = 18 9 = 10 5 => 2 Yes, they are similar teams 1 2 3 4