We are working today and next block on a preview of the first January unit over similarity. Our topic is "dilation". In class today we used Geogebra to do transformations and reviewed rotation around a point, reflection across a line, and translation along a vector. All of these are rigid transformations that keep figures congruent. We then tried dilation with Geogebra - a non-rigid transformation where you transform a figure by moving it by a scale factor away from (or closer to) a center of dilation.
We went through a process in class where we reached conclusions through our investigations to realize: corresponding angles of dilated polygons are congruent, corresponding sides have the same ratio as the scale factor, corresponding sides are either parallel or collinear, a scale factor less than 1 reduces the pre-image to a smaller image, a scale factor greater than 1 enlarges to a larger image, corresponding vertices of images and pre-images are collinear with the center of dilation.
We then did Example B on p 371 on graph paper. When a rule is used that multiplies all vertices by a number, the new figure is a dilation with center at the origin. We:
If you need graph paper, come by and get it or google "graph paper pdf" and you should be able to find and print some online.
1st - 3rd will see their tests next time. If you have not taken the test yet, Tuesday is the last day to do that. Get busy! The semester is almost over.
Next post down has the first final review and the topic list.
This was a tough block to miss because I cannot replace the activity with handouts and information. I have done my best to address everything that I can in this post. I suggest talking to someone who was here. There is no quiz over this content before Christmas.
We went through a process in class where we reached conclusions through our investigations to realize: corresponding angles of dilated polygons are congruent, corresponding sides have the same ratio as the scale factor, corresponding sides are either parallel or collinear, a scale factor less than 1 reduces the pre-image to a smaller image, a scale factor greater than 1 enlarges to a larger image, corresponding vertices of images and pre-images are collinear with the center of dilation.
We then did Example B on p 371 on graph paper. When a rule is used that multiplies all vertices by a number, the new figure is a dilation with center at the origin. We:
- used graph paper to do EX B on p 371, answering all questions
- copied the definition of dilation from the bottom of p 371 into our geometric truth, using a cutout of EX B as our example sketch for the definition
- wrote up the conjecture from p 372: all circles are dilations of each other. Sketch is concentric circles with an arrow pulling the smaller circle to the larger circle.
If you need graph paper, come by and get it or google "graph paper pdf" and you should be able to find and print some online.
1st - 3rd will see their tests next time. If you have not taken the test yet, Tuesday is the last day to do that. Get busy! The semester is almost over.
Next post down has the first final review and the topic list.
This was a tough block to miss because I cannot replace the activity with handouts and information. I have done my best to address everything that I can in this post. I suggest talking to someone who was here. There is no quiz over this content before Christmas.