Angles part 2

''One is twice as larger as the other one", when given this phrase we know what the first angle is twice as big as the smaller angle. For example if they give you only one angle and it's v, you automatically know that the other side is v. Also the obtuse angle has to be 2v, because it is twice as larger as the acute angle. If they say ''One is 5 degrees bigger than the other" you know that the angle measures 5 more degrees, so that angle will measure x+5. You know when to assign a variable, if you do not know what is the angle measure. Corresponding angles are congruent. Vertical angles are also congruent, but supplementary angles are not. Two angles can not be supplementary and corresponding at the same time it can only be corresponding if the angles are across from each other but on different sides of the parallel lines. Two angles can be vertical and corresponding at the same times because corresponding angles are congruent and so are vertical angles. The four angles that are formed around a line and a transversal ALWAYS equal 360 degrees.  

Angles part 1

When you set an equation equal to 90 or 180 you have to  determine whether the angle is 180 or 90 by looking at the angle and seeing if it is 180 or 90 or if it is congruent or not. We we set angles equal to each other in a equation that means that the angles are vertical and or congruent. If we solve for x that doesn't mean that we finished solving for the equation. The answer will not be correct because we have to solve for the missing side not for x. Do you know what congruent means? Congruent means the same. Vertical angles are congruent they are across from each other and they measure the same. Complementary and supplementary angles are not congruent. Angles that are congruent are corresponding angles and vertical angles.

Vertical Angles

Do you know what congruent means? Congruent means when angles have the same measure. When you have vertical angles you automatically know that there are two angles that are across from each other, measuring the same. A quadrilateral is a four sided polygon. If you only have one angle in a intersecting quadrilateral you CAN find the other angles because , they are vertical angles. If one side of the vertical angle is 67 degrees the other side is 67 degrees.

Pythagorean Theorem Wrap-up

In my opinion the Pythagorean Theorem method is very useful because the formula (a^2+b^2=c^2) helps you find the missing side of the right triangle. REMEMBER this formula can only be used for right triangles. The hypotenuse is the longest side of the right triangle opposite of the right angle. The legs however are the smallest sides of the right triangle.
For example, the distance from the corner of the ice ring to the other side is 30 yards. The distance from the corner of the ice ring to the left side of the ring is 40 yards. What is the distance from the corner of the ring to the middle of the ring?

Well first you have to apply the formula a^2+b^2=c^2. Then plug in your numbers for the variables. 30^2+40^2=c^2. Then solve for a and b. 600+1600=c^2. Then you add that and you get 2200. Finally take the square root from both sides. You'll get about 46.9.

"Laws of exponents part 1"

Yes we can expand any variable with an exponent. For example x^2 equals x*x. The exponent of the term is 1. A pattern that i noticed was that every time you multiply variables with exponents you have to add the exponents, for example x^4 * x^3 will equal x^7. You can derive that every time you multiply exponents you have to add the exponents to get your product.