The Similarities Between Shapes
I have three examples for you.
Determine similarities by using transformations
A transformation is an operation that maps a geometric figure, preimage, onto a new figure, image.
A reflection is a transformation where a figure is flipped over a line.
Step 1 - reflect < ABC that's on the left top corner over the Y axis. So that A maps onto A on the bottom right hand corner.
Step 2 - Write the ratios comparing the lengths of each side.
AB/AB = 2/2 or 1, AC/AC = 2/2 or 1, CB/CB = 3/3 or 1
Since the ratios are equal, triangle ABC (on the left side) is the dilated image of triangle ABC (on the right side). So the two triangles are similar because a translation maps triangle ABC (on the left side) onto triangle ABC (on the right side).
The orientation of the figures is different, so one of the transformations is reflection.
Reflect the figure that's on top over the Y axis so that P matches with P at the bottom so that it is oriented the same way as triangle PRQ.
write ratios comparing the length of each side.
PQ/PQ = 2/2 or 1, RQ/RQ = 3/3 or 1, PR/PR
The ratios are equal so the triangles are similar.
Emily enlarges the photo shown by a scale factor of 2 for her web page. She then enlarges the webpage photo by a scale factor of 1.5 to print. If the original picture is 2 inches by 3 inches, what is the the dimensions of the print? Are the enlarged photos similar to the original?
Multiply each dimension of the original photo by 2 to find the dimensions of the webpage photo.
2 in. x 2 = 4 in. 3 in. x 2 = 6 in.
So, the webpage photo with be 4 inches by 6 inches. Multiply the dimensions of that photo by 1.5 to find the dimensions of the print.
4 in. x 1.5 = 6 in. 6 in. x 1.5 = 9 in.
The printed photo will be 6 inches by 9 inches. All of the three photos are similar since each enlargement was the result of a dilation.