Today was a big content day in Pre-AP Geometry.
There are two big ideas that mesh together:
Right triangles (similar) with angles of 30-60-90 degrees have a predictable ratio that can be used to find missing sides: if the short leg is x, the the hypotenuse is 2x, and the long leg is x times the square root of 3. So if you know one side, you can find the other two. Isosceles right triangles (all similar) have angles of 45-45-90 degrees. If the legs of a 45-45-90 are "a" in length, then the hypotenuse is "a times the square root of 2".
We also worked at the algebra required to simplify radicals so that we can keep our answers in exact form, and so we can work better with the "Pythagorean Shortcuts" mentioned above. (2 special ratios)
Our warm-up was to add 7 problems to HW #6 from the old textbook on your desk. I also took a grade on HW #6. If you did not get the remind message, you can show it to me next time.
We went over HW and warm-up and answered questions.
We read in the old textbook about how to tell if a triangle is acute or obtuse (C squared is bigger, then obtuse; C squared is smaller, then acute). Go back to HW #6 and state whether 15-18 on p 502 were acute or obtuse.
We also looked at Pythagorean Triples and put the four main ones in our notes: 3,4,5; 5,12,13; 7,24,25; 8,15,17. All others are just multiples of (similar to) these.
If you are still not on my REMIND, please JOIN MY REMIND RIGHT NOW!! Text to 81010 the message: @msbogart
Take-away: the whole unit is about right triangles and is related to the Pythagorean Theorem. Every problem should be approached: Where is the right triangle? Where is the hypotenuse? Ms. Bogart's fave: every isosceles triangle is just 2 equal right triangles when you put an altitude in it. (add-on problem we did in class).
Another important note: the textbook for this unit is really good at adding meaning, and also usually has examples. You should read each section. It's good stuff!
Notes are attached below over the two shortcuts and some simplifying radicals.
HW #7 is pp 507-8:1-8 PLUS 1-14 on the online "Use your Algebra Skills over "Radical Expressions". To get there, log in to flourishkh.com with your username (first part of email), password: 5 digit lunch code, and pin #: 72703A.
Then do NOT choose Student E-book. Choose "Use your Algebra Skills". Then choose "Radical Expressions" from pull-down menu. Do 1-14 and show work. Examples are there, and some are in my notes. On pp 507-8, do not use the Pythagorean Theorem. Try to find the missing sides with the shortcuts (unless the triangle is not one of the special angle measures).
3rd period - no Radical Expressions because of Tornado Drill.
pre-ap_geometry_notes_and_practice_10.1-2.pdf |