Took assessment on parallel/perpendicular lines on coordinate plane and review topics.
Homework
watch and take notes on this video: direct link
Passed back assessments and went over them with peer experts. Went over the reassessment procedure in more detail. Took a non-sense conditional statement using made up words to rewrite it into the converse, inverse, and contrapositive. Looked at a geometric example and analyzed them for truth or falsehood, noting that the contrapositive always had the same truth value as the original statement. Thought about our own statements with a true converse, which can be combined in something called a biconditional statement. Looked at the differences and inductive and deductive reasoning, leading from conjectures to theorems, and finally at the transitive property which lets you transfer value from one quantity to another. Did our first proof of the congruence of vertical angles.
Notes from board
Homework
p. 36 #16-28
Resources
Statement, converse, inverse and contrapositive: link link2
biconditional statement: link
proving vertical angles congruent: link
Warm up involved writing a converse and then combining it with the conditional statement in a biconditional. Went over homework, then thought about how to prove lines parallel without a grid or slope, and learned the corresponding angles postulate (assumption) through this video here. Reviewed angle relationships through a sudoku-like puzzle dealing with placing labels on angles to meet certain criteria. Then used the corresponding angles postulate to prove the alternate interior angles theorem (see here for similar proof) and then used jigsaw groups to prove 4 more theorems (alternate exterior angle, same side interior, converse of alt int, and converse of same side int). Added these to our theorems booklet.
Notes from board
blank copy of handout (see last slides in notes for completed versions)
Homework
p. 87 #1-15 (odds only)
Resources
angle relationships: corresponding, alternate interior, same side interior: link 1 link 2
corresponding angles and algebra: link
alternate interior angles and algebra: link