What’s Goin’ On In Room 133

Posts Tagged ‘geometry’

Homewoork to date: p.442 q1-5, then we assigned #5-10, along with calculating the perimeters of figures used in questions #8, 10 and 11.  We have also used both dot and graph paper to create similar pairs of triangles and quadrilaterals.  In all of these we now see how proportion and ratios work to aid our calculations.

Our review took us through all of the basic geometry figures: points, lines, planes, line segments, rays and angles.  We discussed how these angles are classified (in other words, which angles are which?) and we covered acute and obtuse angles, right angles and straight angles and even a little bit of reflex angles.  (Gotta save something for Mr Jackson to do next year !

We covered the various forms of triangles – acute, right, obtuse, equilateral, isosceles and scalene.  And we know there are no corners on any of these figures because in math these points are known as vertices (or in signular form, the vertex).  We know the difference between a right triangle, an isosceles traingle and a right isosceles triangle.  We know that all triangles have 180 interior degrees within the figure, and we know that an isosceles triangle will have two sides that are congruent along with two congruent angles, and we know an equilateral triangle has all sides and consequently all angles congruent.

We know a lot.  Tomorrow we’ll talk a little about quads.  Got to get on stage.  Rock on, colleagues.

I think I feel another oldie coming on.  Remember “Earth Angel”?  Chocolate to the first ones who hum a few bars on our next get-together!

But the word “geometry” is derived from two Greek words that literally mean “earth measure”.  And that should lead you to see that there is a real and very practical purpose behind making sure that you know the difference between rectangle and a rhombus, that you know how to calculate the missing angle if given only two angle measurements of a triangle or only three angle measurements of a quadrilateral.  You need to know what parallel lines are and what they mean to the form of the figure (the shape of the polygon) on your sheet.  Surveyors and mapmakers (cartographers) use this stuff all the time.  That’s how the building you are sitting in got built where it is in the first place – someone sat down and “did the math”!

All of this has always been about trying to make measurements across the landscape of the earth.  In fact, a lot of this was used to make measurements across the SEAscape of the planet as well.  After all, Columbus never had a GPS – at least not one based on man-made satellites, anyway ; )!

Rock on, colleagues!  (And Happy Valentine’s Day!  —But don’t forget my homework on page 442, questions 1-5.  And if you have been away for a while, you’ll need to knock out pages 436-437, questions 10-32.  Do a good job wit the ‘art’ question #27 – make it nice and colorful!)

We usually hear that phrase coming from the lips of one who is looking at a deal and is trying to figure out what’s in it for the other guy…sort of like what we do when we’re talking to telemarketers (that is, when we are trying not to be rude by just hanging up..you don’t do that do you?) 

Anyway, after today, you now know about all kinds of angles!  The right angle (90 degrees), the acute and the obtuse angles  (lesser and greater than 90 degrees respctively), the straight angle (180 degrees) and the reflex angle (greater than 180 degrees).  But there are so much more…the supplementary angles (an adjacent pair that add up to 180 degrees), the complementary angles (an adjacent pair that adds up to 90 degrees), and vertical angles (we called them opposite angles in class and they are equal to each other when two lines intersect). 

Those last angles, since they are equal to each other, can also be said to be congruent.  Angles that are the same are congruent.  That word also works with the lengths of a line.  Two lines are said to be congruent if they are equal to each other in length.  Like the sides of a square are congruent; the opposite sides of a rectangle are congruent, and so forth.

So what’s so cool about knowing this stuff?  Well, besides having an advantage when you’re playing pool with your kid brother, angles help you figure out all kinds of neat stuff.  Do you know that you can figure out the height of a building by just by using angles?  Oh yeah.  And the captains of the high seas used to navigate the waters by taking angles across the stars!  In fact, GPS is still using those same principles today.  Talk about out of this world!  Anyway, keep working on those definitions and examples, and knock out the rest of on page 424.  And rock on, colleagues!