Tests on geometric foundations were returned and discussed; we spent the first part of class working on error analysis, which is required for all missed problems. Complete corrections with explanations can earn back up to half of the points missed on the test.
We then moved on to our first geometric proof, which proved the claim made earlier that if angles are vertical angles, then they are congruent. This video shows the proof we did in class.
We then investigated the 8 angles formed by two lines crossed by a transversal. We noticed that angles that are in the same or matching position have a special relationship, and that these angles are called Corresponding Angles. When we measured with our protractors, these corresponding angles were not the same measure, because our two lines were not parallel.
Next, we drew two parallel lines crossed by a transversal and then measured the matching pairs of angles--now these corresponding angles were indeed the same measure according to the protractor.
Finally, we looked at the parallel picture again and were able to figure out all 7 missing angle measures after being given only one of them to start with. See these tutorials for more assistance.
http://www.mathopenref.com/anglescorresponding.html
http://www.mathopenref.com/tocs/paralleltoc.html
Homework: Test Corrections due next class period
**make a personal glossary of the list of words on pg 202, and include a drawing or diagram with each definition.
Thursday/Friday
We started with a journal prompt examining the proof from the last class: If two angles are vertical angles, then they are congruent. Is the converse true or false? Meaning, is it true or not that if two angles are congruent, then they are vertical angles? We described our reasoning independently.
After the journal we looked at a real-world geometry example that involved making sure the panes of a window lined up properly. Here are the lecture notes from today.
We next moved on to two separate proofs, each of which build upon our idea of Corresponding Angles from yesterday. We proved that alternate interior angles of parallel lines are congruent (video here, showing the same method) and that same-side interior angles of parallel lines are supplementary (video here). Finally, we did an example of proving two lines parallel from two other parallel lines (making a "hashtag" figure) which involved several of these ideas strung together. Here is a summary of that procedure: video (starts at 3:12).
Finally, we did a geometric construction of a line parallel to a given point not on a given line. Here is that procedure:
Homework: p 202: #6-21
p 202 203 204
***Vocabulary Quiz on Monday***
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