Warm up was a logic puzzle dealing with converses, inverses, and contrapositives [see here for something similar]. Passed back tests on coordinate geometry. Went over angle relationships with a 'sudoku' type puzzle [blank copy here] where angle labels had to be placed to meet certain criteria. Reviewed how to prove lines parallel in Cartesian geometry with slopes and contrasted that with Euclidean geometry where there is no grid to find slope. Introduced the corresponding angles postulate [video here], then reviewed the proof of vertical angles being congruent from last week, to finally prove that alternate interior angles are congruent [similar proof here]
Notes from board
Homework
p. 87 #1-7 [CO-C9b]
Resources
angle relationships in hw: corresponding, alternate interior, same side interior: link 1 link 2
corresponding angles and algebra: link
alternate interior angles and algebra: link
Warm up took the theorem proved last Thursday/Friday and formed its converse, inverse, and contrapositive and found which were true or false (and showed the false ones with counterexample). Went over homework, then constructed parallel lines in Euclidean space with compass and straight edge (demonstrated here). Used a protractor to measure one of the angles (shown here) and then logically deduced all of the remaining angles (here). Worked through a proof example (see notes), and then did jigsaw groups to prove 4 additional theorems.
Notes from board
Homework
p. 35 #28-32 [CO-C9a]
p. 87 #12-16 [CO-C9b]
Resources
writing a converse, inverse, and contrapositive: link
Proving lines parallel: link
Warm up dealt with proving two lines parallel by using a pair of given congruent angles (similar problem here). Went over homework, then explored the angle relationships within triangles. Cut and tore triangles to show that the three angles make 180° (demonstrated here) and then proved this using Euclid's fifth postulate along with alternate interior angles of parallel lines, which was a theorem proven on Monday. (complete proof here) Applied this fact to solve for missing angles in an 'angle chase' handout. Passed out practice assessment at the end of class.
Notes from board
Homework
Work on practice assessment [blank copy here] [SOLUTIONS HERE]
Assessment on these topics is Monday
Resources
Converse and contrapositive: link
proving vertical angles congruent: link
finding all the angles in a parallel set cut by transversal: link
proving lines parallel: link
segment addition postulate with midpoint: link