Over the weekend, April 24th was Armenian Genocide Remembrance Day. President Biden became the first U.S. leader to acknowledge the date.
Of course, the main holidays I acknowledge on the calendar are those related to school calendars. Last year, the LAUSD stated that April 24th would become a district holiday starting in 2021-22, with all schools closed that day.
But a proposed LAUSD calendar for 2021-22 shows no extra day off in late April. Instead of subtracting a day, the district has been considering adding ten extra days to the calendar to make up for learning lost due to the pandemic. These proposals include starting a week earlier and reducing the usual three-week winter break to two weeks, or starting two weeks earlier. No proposal has an extra April holiday.
Then again, we might point out that April 24th, 2022 will fall on a Sunday. Perhaps more effort will be made to observe the April date in 2023, when the 24th will fall on a Monday.
In the past, I pointed out that late March and late April are excellent times for new federal holidays. There are no federal holidays between Presidents' Day and Memorial Day (which explains why there's a Big March, a long stretch with no day off from school). In creating the months of the Eleven Calendar, I notice that many federal holidays are approximately one-eleventh of the year apart (such as Memorial Day to Independence Day, or MLK Day to Presidents' Day). Thus there's room for two federal holidays between Presidents' Day and Memorial Day.
The two newest LAUSD holidays, Cesar Chavez Day and Armenian Day, fit right around the times when I think there should be new holidays. Of these two dates, April 24th is more controversial. There was backlash in Turkey when Biden made his announcement, and some Turkish-Americans in Southern California have expressed concern with the new holiday.
(There should also be an extra holiday in early August, between Independence and Labor Day. Canada has a Civic Holiday on the first Monday in August -- this is normally summer break, but it's also the first day of school under one of the LAUSD proposals.)
We might instead consider a more internationally neutral late April holiday. Earth Day is on the Adam of Armenian Day, while National Arbor Day is on the last Friday in April (that is, the Friday on or after Armenian Day). Also, Administrative Professionals Day is on the third Wednesday in April (the Wednesday before Earth Day), but I don't see anyone going for a Wednesday off from school. (Notice that either Admin Day or Arbor Day would also fit the Andrew Usher Calendar as well.)
My LA County district was closed today, but this wasn't in an effort to observe Armenian Day. Instead, it's a floating holiday to ensure that finals week is Days 178-180. Meanwhile, high schools in my new Orange County district were asynchronous today to prepare for the transition from two to four in-person days per week.
And speaking of my new district, at least one high school (the one for which my long-term middle school is a feeder) has announced that the SBAC will be this week. This is perfect timing for the blog, since today's Lesson 15-3 -- on inscribed angles -- is typically the last lesson in our text that will appear on the SBAC.
Oh, and today is the birthday of Anne McLaren, a British biologist. I try to acknowledge Google Doodles for scientists here on the blog.
Inscribed Angle Theorem:
In a circle, the measure of an inscribed angle is one-half the measure of its intercepted arc.
Given: Angle ABC inscribed in Circle O
Prove: Angle ABC = 1/2 * Arc AC
Proof:
Case I: The auxiliary segment
Notice that the trick here was that between the central angle (whose measure equals that of the arc) and the inscribed angle is an isosceles triangle. We saw the same thing happen in yesterday's proof of the Angle Bisector Theorem -- the angle bisector of a triangle is a side-splitter of a larger triangle, and cutting out the smaller triangle from the larger leaves an isosceles triangle behind.
Let's move onto Case II. Well, the U of Chicago almost gives us a two-column proof here, so why don't we complete it into a full two-column proof. For Case II, O is in the interior of Angle ABC.
Statements Reasons
1. O interior ABC 1. Given
2. Draw ray BO inside ABC 2. Definition of interior of angle
3. Angle ABC = Angle ABD + Angle DBC 3. Angle Addition Postulate
4. Angle ABC = 1/2 * Arc AD + 1/2 * Arc DC 4. Case I and Substitution
5. Angle ABC = 1/2(Arc AD + Arc DC) 5. Distributive Property
6. Angle ABC = 1/2 * Arc AC 6. Arc Addition Property and Substitution
The proof of Case III isn't fully given, but it's hinted that we use subtraction rather than addition as we did in Case II. Once again, I bring up the Triangle Area Proof -- the case of the obtuse triangle involved subtracting the areas of two right triangles, whereas in the case where that same angle were acute, we'd be adding the areas of two right triangles.
"In proving the theorem for each of these two more general special cases, the truth of the theorem for the special case was used in the proof."
Here's the rest of what I wrote two years ago:
The text mentions a simple corollary of the Inscribed Angle Theorem:
Theorem:
An angle inscribed in a semicircle is a right angle.
The text motivates the study of inscribed angles by considering camera angles and lenses. According to the text, a normal camera lens has a picture angle of 46 degrees, a wide-camera lens has an angle of 118 degrees, and a telephoto lens has an angle of 18. I briefly mention this on my worksheet. But a full consideration of camera angles doesn't occur until the next section of the text, Lesson 15-4 -- but we're only really doing Lesson 15-3 today.
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