Sunday, November 18, 2012
Math Help Needed?
If you have math help that just tell me what you want me to go over in the comments andI shall review it for you. Comment!
Friday, November 9, 2012
Definition of Supplementary Angles
Supplementary angles are extremely easy to understand. All that supplementary angles are, are two angles that equal 180 degrees.
<4 and <1 are supplementary.
<8 and <3 are supplementary.
<7 and <8 are supplementary.
If you have any questions, then, as usual, just comment!
<8 and <3 are supplementary.
<7 and <8 are supplementary.
If you have any questions, then, as usual, just comment!
Thursday, November 8, 2012
Definition of Linear Pairs
Linear pairs are basically two angles that are adjacent and form a line. Adjacent simply means that they share a side.
<1 and <4 form a linear pair.
Linear pairs are supplementary angles,meaning that when added together the form 180 degrees. One thing that you have to remember is that linear pairs have to form lines. <1 and<4 form line l.
<1 and <3 form a linear pair. They form line t.
<2 and <7 form a linear pair. They form line m.
There are a few more, see if you can find them!
If you have any questions than comment!
 |
| Source |
Linear pairs are supplementary angles,meaning that when added together the form 180 degrees. One thing that you have to remember is that linear pairs have to form lines. <1 and<4 form line l.
<1 and <3 form a linear pair. They form line t.
<2 and <7 form a linear pair. They form line m.
There are a few more, see if you can find them!
If you have any questions than comment!
Wednesday, November 7, 2012
Definition of Vertical Angles
Vertical Angles are formed when you have intersecting lines:
Vertical angles, plain and simple, are the angles opposite of each other. The second thing that you have to know is that vertical angles are congruent, they have the same measure.
<1 and <8 form a vertical pair.
 |
| Source |
<1 and <8 form a vertical pair.
If <1=70, then <8=70 as well.
<2 and <5 form a vertical pair.
<3 and <4 form a vertical pair.
<6 and <7 form a vertical pair.
As usual, if you have any questions just comment!
Monday, November 5, 2012
Point, Plane, and Line Postulates
This is a series of pretty basic statements, so just hang in there.
1.) Any two points make a line. No matter where those two points are, they will always* make a line. Also, whenever you label a line, you label it with two points.
2.) When you have two intersecting lines, where they cross is exactly one point, no more, no less.
3.) Any three points that are non-col-linear make up a plane. A plane is always labeled with three points. A plane contains 3 or more points but is only labeled with three.
4.) If two points lie within a plane, then the line they form is also in the plane.
5.) If two planes intersect, they form a line at the intersection. If three insect, the intersection is a point.
If you have any questions, just ask of course!
1.) Any two points make a line. No matter where those two points are, they will always* make a line. Also, whenever you label a line, you label it with two points.
2.) When you have two intersecting lines, where they cross is exactly one point, no more, no less.
3.) Any three points that are non-col-linear make up a plane. A plane is always labeled with three points. A plane contains 3 or more points but is only labeled with three.
4.) If two points lie within a plane, then the line they form is also in the plane.
5.) If two planes intersect, they form a line at the intersection. If three insect, the intersection is a point.
If you have any questions, just ask of course!
Sunday, November 4, 2012
Segment Addition Postulate
The Segment Addition Postulate is a very simplistic geometry term. All that the Segment Addition Postulate is saying is that when you have three co-linear points, the first piece of the segment, plus the second equals the whole. To clear that up a bit:
___ ___ ___
AB + BC = AC
Questions? Comment!
Definition of Midpoint
If you have gotten to algebraic proofs, then this is for you. To help demonstrate this, we have a diagram:
Pretty much it's saying that If you are given the midpoint, 'B', then it's safe to say that one half of the line segment, 'AB', equals the other, 'BC'.
The two hash marks, one being between A and B, the other being between B and C, just show us that those two segments are congruent. The Definition of Midpoint states that:
___
If B is the Midpoint of AC then
___ ___
AB = BC
Pretty much it's saying that If you are given the midpoint, 'B', then it's safe to say that one half of the line segment, 'AB', equals the other, 'BC'.
Saturday, November 3, 2012
Subtraction, Addition, Multiplication, and Division Properties
These properties are all pretty much the same things so I've decided to put them all in one post.
The Addition Property is when you add something to both sides of an equation such as when you are solving an algebraic equation:
x-3 = 9
+3 +3 <---
x = 12
Did you catch that?
The Subtraction Property is when you subtract something to both sides of an equation such as when you are solving an algebraic equation:
The Addition Property is when you add something to both sides of an equation such as when you are solving an algebraic equation:
x-3 = 9
+3 +3 <---
x = 12
Did you catch that?
The Subtraction Property is when you subtract something to both sides of an equation such as when you are solving an algebraic equation:
x+5 = 9
-5 -5 <---
x = 4
See? Pretty simple.
The Multiplication Property, as you may be able to guess by now, is when you multiply something to both sides of an equation such as when you are solving an algebraic equation:
x/4 = 2
*4 *4 <---
x = 8
Piece of cake.
The Division Property is when you divide something to both sides of an equation such as when you are solving an algebraic equation:
4x = 8
/4 /4
x = 2
x/4 = 2
*4 *4 <---
x = 8
Piece of cake.
The Division Property is when you divide something to both sides of an equation such as when you are solving an algebraic equation:
4x = 8
/4 /4
x = 2
Remember, if you have any questions, comment.
Transitive Property of Equality
The Transitive Property of Equality is a little more difficult than the other two, although still very simple. The important thing that you have to remember about the transitive property is that the order in which the terms are stated is very important. The Transitive Property of Equality states that:
If a=b and b=c, then a=b
Another example, perhaps a little more applicable would be:
If 5x+4=4x+8 and 4x+8=24, then 5x+4=24
As I said before, order is important. If you look at the example it fits into the correct order.
The 'a' term is the '5x+4'. The 'b' term is the '4x+8'. And lastly, the 'c' term would be the '24'. The example above fits neatly into format.
If |5x+4| = |4x+8| and |4x+8| = |24|, then |5x+4| = |24|.
If | a | = | b | and | b | = | c |, then | a | = | c |.
See how that works?
If the equation had been:
If |5x+4| = |4x+8| and |24| = |4x+8|, then |5x+4| = |24|.
| a | = | b | and | c | = | b |, then | a | = |24|.
It would not be Transitive. See how that came out as:
If a=b and c=b, then a=c. Which is incorrect. Do you see the difference between that and
If a=b and b=c, then a=c
If you have any questions, comment!
If a=b and b=c, then a=b
Another example, perhaps a little more applicable would be:
If 5x+4=4x+8 and 4x+8=24, then 5x+4=24
As I said before, order is important. If you look at the example it fits into the correct order.
The 'a' term is the '5x+4'. The 'b' term is the '4x+8'. And lastly, the 'c' term would be the '24'. The example above fits neatly into format.
If |5x+4| = |4x+8| and |4x+8| = |24|, then |5x+4| = |24|.
If | a | = | b | and | b | = | c |, then | a | = | c |.
See how that works?
If the equation had been:
If |5x+4| = |4x+8| and |24| = |4x+8|, then |5x+4| = |24|.
| a | = | b | and | c | = | b |, then | a | = |24|.
It would not be Transitive. See how that came out as:
If a=b and c=b, then a=c. Which is incorrect. Do you see the difference between that and
If a=b and b=c, then a=c
If you have any questions, comment!
Symmetric Property of Equality
The Symmetric Property of Equality is another extremely simple property. This is one that tends to catch people up on proofs because it is so simple that you just skip over it in your head. The Symmetric Property of Equality states that:
If a=b, then b=a.
A more applicable example is:
If 4x+5=13, the 13=4x+5
Questions? Comment.
If a=b, then b=a.
A more applicable example is:
If 4x+5=13, the 13=4x+5
Questions? Comment.
Reflexive Property of Equality
This is quite possibly the easiest of the properties. The Reflexive Property of Equality states that:
a=a
Pretty basic. A more applicable example would be:
7a+8=7a+8
Questions? Comment.
a=a
Pretty basic. A more applicable example would be:
7a+8=7a+8
Questions? Comment.
Friday, November 2, 2012
Properties
One of the most annoying things about Geometry is trying to remember all of the properties. Properties are Math's way of naming the simple steps that most of us do in our heads. I am going to explain a few in the following posts.
Subscribe to:
Posts (Atom)