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Table of contents

Triangle: A polygon with three sides. Triangles also have three angles. We have already stated that the sum of the angles of a triangle is degrees. Later on in this chapter, we will give a sample proof from geometry. Triangles can be classified two ways: by sides and by angles.


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A scalene triangle is a triangle that has three unequal sides. It also has three unequal angles. The ever popular isosceles triangle is a triangle with two equal sides. AB and BC are the legs. They are equal.

Bob Miller's Basic Math and Pre-Algebra for the Clueless, 2nd Ed.

They are also equal. The base is AC. It can be equal to a leg, but it usually is larger or smaller. It can equal a base angle, bigger than a base angle if the base is bigger than a leg, or is smaller than a base angle, if the base is smaller than a leg. All angles are equal.


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Triangles can also be classified according to angles. The side AB opposite the right angle C is called the hypotenuse.

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The sides, BC and AC, opposite the acute angles are called legs. They may or may not be equal. An obtuse triangle is a stupid triangle.

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Just a joke. Triangles can be a combination of the two. Acute and scalene B. Right and scalene C. Obtuse and scalene D. Acute and isosceles E. Right and isosceles F. NOTE There is only one equilateral, acute equilateral, since all the angles must be 60 degrees. Most geometry and trig word problems are very easy. We will do more problems on triangles when we get to later chapters. In regular geometry, many weeks are spent on triangles.

We will do more on triangles later, but not nearly as much as you would find in geometry. Theorem: a provable law. Postulate: a law taken to be true without proof. Postulate: Through a point not on a line segment one and only one line can be drawn parallel to another line segment. If two lines are parallel, alternate interior angles are equal.

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See the Z and the backward Z?!!!! Look at the picture; this says the sum of the angles of a triangle is degrees!!! Believe it or not, the way you think through a proof is the way you answer an English essay or a history essay. Only if you become a major in math or mathrelated areas will you do a lot of proofs. Maybe, with the help of my books, you will become so good at math you will want to do things with it. Math is incredibly wonderful, but to get to the point where you can see how great it is, you must learn your basics well!!!!! NOTE It would be nice to know all the following because most come up over and over and over, but I would not sit down to memorize them; just keep the list in front of you.

You will be surprised how many you will soon know. Two primes on the inside become one on the outside. There are two square roots that we want to know the approximate value, because they come up so much!!! My Aunt Betty one of two once lived at I could never forget that house number!!! We wish to combine terms; it is the same as adding subtracting like terms!!!!! It is silly to multiply out first, because you then have to break it down; break it down at once!!!! A little division. The following are called Pythagorean triples.

The side listed last is the hypotenuse. Also 8,15,17 and 7,24, Are there any more? Yes, an infinite number.

Some are 9,40, Why should you memorize only the nine? The other three I listed have come up once every 7 or 8 years. We cannot memorize everything. We have to memorize the most important ones. Find the hypotenuse. This is to trick you.

Bob Miller's Calc for the Clueless: Precalc (Bob Miller's Clueless Series)

The missing side is not 4. It comes from a square. The legs are equal. Leg to hypotenuse? Hypotenuse to leg? In geometry you will show that both triangles are the same. Always get the short leg first, if it is not given.

Bob Miller's High School Calc For the Clueless - Honors and Ap Calculus Ab & Bc

Short to hypotenuse? Hypotenuse to short? Short to long? Long to short? I am not sure who needs this chapter, but everyone needs these facts at some time. All quadrilaterals have two diagonals, a line drawn from one vertex to the opposite vertex.

Bob Miller's Calc for the Clueless: Precalc - Bob Miller - Häftad () | Bokus

In the figure on the side, AC and BD are diagonals. There are many kinds of quadrilaterals. One is a parallelogram. Parallelogram: a quadrilateral with the opposite sides parallel.