Warm up introduced the idea of similarity by recognizing if shapes are similar and finding a missing side length by setting up proportions when given similar shapes. Briefly looked at what we're learning this quarter, then defined similarity and looked closely at relationship in scale factor when dilating a shape (noting that if the linear scale is some number k, then the area is scaled by factor k^2). Defined dilation and compared it to rigid motions and then did both a Euclidean (compass-straight edge, blank plane) and Cartesian (coordinate plane) dilation.
Notes from board
Homework
p. 255-6: #1,4,10
Resources
dilation on the coordinate plane: link1 link2 (starts at 2:15)
dilation and area ratios: link
determining scale factor on coordinate plane: link (first half of it)
determining if similar; finding missing sides given similarity: link1 (made by me!) link 2
Warmup was a problem dealing with identifying correct proportions for similar triangles and finding the point(s) to make two triangles similar. Went over homework, then learned how to dilate figures on the coordinate plane when the origin is not the center of dilation. It can be thought of as using the grid or slope (change in y and change in x) to determine the locations of the dilated figure's coordinates. Also worked backwards to figure out the location of the center of dilation and scale factor given two similar shapes on the coordinate plane.
Introduced the idea of triangle similarity criteria and looked at examples of the 3 laws, SSS~, AA~, and SAS~. Some classes began practicing with multiple choice questions identifying why two triangles are/aren't similar.
Notes from board
Homework
p. 260 #7-14
Resources
dilating around a non-origin point, same problems from class: link
determining scale factor from dilation NOT around origin: link (by me :)
determining if two triangles are similar, criteria: link 1 (by me!) link2