tag:blogger.com,1999:blog-6651514617266100245.post6441451068049711702..comments2024-01-03T04:58:04.221-05:00Comments on I Hope This Old Train Breaks Down...: Thinking AloudUnknownnoreply@blogger.comBlogger1125tag:blogger.com,1999:blog-6651514617266100245.post-17338037000530794122012-03-20T13:23:33.702-04:002012-03-20T13:23:33.702-04:00There's lots of good stuff you can do with thi...There's lots of good stuff you can do with this. Example. If we call the point of intersection of the first two parallels D, then ABDC is a parallelogram. Its diagonal divides it into congruent triangles whose area must be the same. But if we know already that a pgram has area of base times height, we see that, for any triangle, its area is half base times height.<br /><br />Another example. One pair alt int: ABC and DCB. A second pair: DBC and ACB. Angle addition gives us that angles ABD and ACD are congruent. Third angle theorem proves that angle BAC = angle BDC. Conclusion: in a pgram, opp angles are congruent.<br /><br />A final example. Extend side AB upwards. Another pair of alt int angles are created. The three angles at B sum to 180. Thus the three angles of triangle BCD sum to 180. Bingo - the triangle angle sum theorem.<br /><br />Fun fun.Dr. Mhttps://www.blogger.com/profile/00209597695197799059noreply@blogger.com