Proving Circles are similar
- Deborah Lebair
***This assignment includes an on-line CANVAS submission ***
In the first semester we talked about transformations which produced congruent and similar figures. See if you and your neighbor can remember which transformations produced which kinds of figures. Write these on your accompanying worksheet in the spaces provided. We are going to prove circles are similar using transformations, but first let's practice on a pair of triangles. I will give you the coordinates for the triangles in the applet below. You will construct them using Geogebra, then experiment and decide which transformations (2) will map ABC onto JKL. You can select and move any figure you construct. Don't forget you can also zoom out or you can pan the coordinate plane across with the move graphics view button (top button on right) in order to see all of your figures. If there is a scale factor involved, be sure to record it and your transformations on your worksheet.
Applet 1: Triangle ABC: A(-2, 7), B(-2, 3), C(1,3) Triangle DEF: D(3,7), E(3, -1), F(9, -1)
Now we are going to prove two circles are similar using the same method. You can construct the following circles in the applet below. Be sure to record the transformations which you used to map the first circle onto the second onto your worksheet.
Applet 2: Circle 1: center at (0,2), r = 3. Circle 2: center at (5,3), r = 9.
For this example, I will give you the coordinates for the center of each circle, and an endpoint for each radius. It is up to you to find the lengths of the radii, and decide on the transformations needed to map one circle onto the other. Use your worksheet and a compass to plot the points and construct the circle. Circle 1: center (0,0) point on circle (2,3) Circle 2: center (10,2) point on circle (18, 14) There are many ways to obtain the length of the radius.
Given the centers and one point on the circle, find the transformations which will map the first circle onto the other.
Circle 1: center (-7, 5) radius other endpoint(1, -9) Circle 2: center (-3,10),radius other endpt (6,-11)
In CANVAS, answer this question: Given two circles, how can I prove they are similar? Please turn in your worksheet when you are finished.