Today we got into the idea that if two triangles are congruent by a shortcut, then there are three other pieces of information in the triangles that are also congruent. This allowed us to prove that "Base angles of an isosceles triangle are congruent." The fill-in-the-blank proof that we did in class is attached below.
All of the shortcut conjectures need to be written up. They are attached below. The sketches can come from the bottom of p 219, or just copy mine from the attachment.
The homework for next block is HW #4: pp 227-8:1-15 (write which triangles are congruent by which shortcut) and 5 of these are cannot be determined. Also do p 218:19-20 (find missing angles). And get all conjectures 25-28 written up.
We practiced simple SSS and SAS shortcuts, as well as realizing that SSA is not adequate for congruence.
We investigated ASA by doing p 169:3. Then we argued from here that third angles are also congruent, so SAA is also true.
We verbally explained the example at the top of p 230 by a combination of partner sharing and class discussion.
Most classes saw their quizzes. They will be returned next time we meet.