No school for Labor Day.
Tuesday/Wednesday
Assessment over GPE-B6a and some review skills. Investigation lesson on parallel lines and angles created by a transversal. Measured a model in a real-world problem (p. 73-76 in textbook) to discover relationships among corresponding angles, alternate interior angles, and same-side interior angles. When the lines are parallel, some repeated structures are created that make these special relationships.
Here are some videos to help you illustrate:
Corresponding Angles video: https://www.youtube.com/watch?v=b49JnSpiogE
(we treat this as a postulate; a simple assumption)
Alternate Interior Angles: https://www.youtube.com/watch?v=tPZwDatpxBA
(notice how vertical angles being congruent, something we've already proven, is used here along with corresponding angles)
Same-Side Interior Angles: https://www.youtube.com/watch?v=2v55h3o1ucw
(also uses vertical angles and corresponding angles)
Some vocab from the board: picture link
Homework: p. 77: 8-11, 15-20 (CO-C9b)
Resources (in addition to video above)
exercise similar to class discussion: https://www.youtube.com/watch?v=gRKZaojKeP0
Finding angle measures; https://www.youtube.com/watch?v=2WjGD3LZEWo
alternate angles: https://www.youtube.com/watch?v=-BPdBfwFgUM
transversal applet: http://mathopenref.com/transversal.html
corresponding angles applet: http://mathopenref.com/anglescorresponding.html
same side interior applet: http://mathopenref.com/anglestransinterior.html
alternate interior angles applet: http://mathopenref.com/anglesalternateinterior.html
Warm up on partitioning a line segment into a ratio into fifths by using the ratio method. (similar to this video). Worked on error analysis of previous class' assessment--analysis must be turned in when re-assessing. Constructed a perpendicular bisector using compass and straight edge using this procedure and then measured points on the bisector to conjecture that all points on this line are the same distance to the endpoints.
Then measured and made a line parallel to a given line using the protractor in a real-world scenario, which illustrated the converse of the corresponding angles postulate: If corresponding angles are congruent, then two lines are parallel. Completed a two-column proof this concept to illustrate use of the transitive property to show congruence and parallelism.
Homework: p. 87: #8-11, 14, 16 (CO-C9b)
Resources: Perpendicular bisector construction: http://www.mathopenref.com/constbisectline.html
using converses to prove lines parallel: https://www.youtube.com/watch?v=a4ZR165Y2JQ (uses "consecutive" instead of "same side" interior angles.)
lesson showing how to set up and solve algebra problems related to this topic: https://www.youtube.com/watch?v=ubDalX0vokQ
more examples and intuitive descriptions: https://www.youtube.com/watch?v=d8Ogo-xiOxs
making sense of complex line diagrams: https://www.youtube.com/watch?v=aq_XL6FrmGs
more specific homework help:
- Examples for #8 and 9: https://www.youtube.com/watch?v=_Qb2VKYfkCw
- Example for #10 https://www.youtube.com/watch?v=2WjGD3LZEWo
- For #11 https://www.youtube.com/watch?v=isFL4LZXXfU
- Similar to #14 https://www.youtube.com/watch?v=PixCGXP7JoM
- #16 is sort of common sense, but the first two minutes of this video show how: https://www.youtube.com/watch?v=sGF3a-dqDBg