Gabby+B

__**Notes for Chapter 9**__ []

**9.1 Goals:** to find squares and square roots, and estimate square roots **9.1 Vocabulary:** perfect square, square root, and radcial sign

**Notes for 9.1:** **page 436-440** To find the square root of something you have to find the number closest to it that can make a perfect square. x2=x*x. For example- the positive square root of 25 is 5, because 5 makes a perfect square for 25, and the positive square root of 49 is 7. But if you had a negitive square root for 49, it would be -7. A square root is the oppostie of a number being squared. 1^2=1   2^2=4     3 ^2=9      4^ 2=16        5^2=25 All of these are perfect squares 6^2=36     7^2=49  8^2=64  9^2=81  10^2=100

**9.2 Goals:** Solve equations by finding square roots and identify and compare numbers in the real number system 9.2 Vocab: Real numbers and irrational numbers

** Notes for 9.2: ** page 441-446 (look in ch 2) Irrational numbers- numbers that are like pi-3.14 and 0.010110111, cannot be written as a fraction Rational numbers-are numbers like 0.2222222(repeating) or 0.6. Even 1/3, anynumber that can be writen s a fraction. (pi cant be written as fraction) I rrational numbers-don't repeat or terminate R eal numbers-a set of rational and irrational numbers Natural numbers- numbers lik 2, 5, and 25. Whole numbers- 0, 1, 8, and 6. Integers - numbers that include 3, -7, 4, and -12. 42/14 is a fraction, but it is also a integer and rational number since it is equal to 3. 5 is a natural number, a whole number, integer, and rational n umber A repeating number would be a rational number since 0.8888(repeating) is equal to 8/9 -7 is a integer, a rational and a real number C omparing numbers on a number line- change the place mark to and inequalaty and the numbers to decimals to see which is bigger. solve equasions by finding square roots- if an equasion has an irrational number for its solution you can find the square root of each side. C omparing numbers on a number line- change the place mark to and inequalaty and the numbers to decimals to see which is bigger. solve equasions by finding square roots- if an equasion has an irrational number for its solution you can find the square root of each side. You can use...... P .....................S  E .....................A  M .........or.........D  D .....................M  A .....................E  S .....................P

9.3 goals- Measure and draw angles, and classify angles as acute, right, obtuse, or straight

**9.3 vocabulary** - point, ray, line, angle, vertex, side degree,protractor, acute angle, right angle, straight angle, and obtuse angle

**__9.3 notes--__** 2 rays ---> that come together at a vertex make an angle. right- 90 degree angle acute- less then 90 degree angles obtuse- larger than 90 degree anlge reflex angle- larger than 180 degrees

**__9-4__** **__goals__** __-__ identifying triangles!!! and finding missing angle measurements.. **__9.4 vocabulary__** - line segment, triangle, vertex, acute triangle, obtuse triangle, right triangle, congruent, scalene triangle, isosceles triangle, and equilateral triangle **__9.4 notes-__** acute-angles are less then 90 degreesright- has t o have a right angle obtuse- at least 1 angle larger then 90 degrees (bc if theres more than 1 obtuse it cant b a triangle--angle sum has to add up to 180 degrees..) scale ne -no sides equal isoscel es - (i remeber this becasue it has "sos" so it has 2 of the same sides, and 1 different) 2 sides are the same and one is different. equalateral -all sides are equal pythagorean theory--only works for right or equalaterall???? A^2+b^2=c^2 hypotanuse-side opposite of t he right angle

**__9.5 goals--__** Use the Pythagorean Theorem to find the length of a side of a right triangle, Use the converse of the Pythagorean Theorem to determine whether a triangle is a right triangle.

**__9.5 vocab--__** legs, hypotenuse, Pythagorean Theorem, converse, solving a right triangle

**__9.5 Notes--__** pythagorean theorum- works with right triangles only, named aftter the guy who figured out A^2+B^2=C^2 C is the hypotanuse (opposite right angle/longest line) "as the crows fly" being able to go diagonal instead of arround the perimiter makes it a shorter length.....route so the A side squared (times itself) plus the B side squared equals the C side--the diagonal length then you find the square root of A^2+B^2 and the square root is C                                                                                          A and B are the sides(also known as the legs) that make up the right angle Each side reduced is 3, 4, and 5 6^2+8^2=10^2 (36+64=100) c=10 the legs of the triangle can't add up to be more than the hypotanuse

**__9.6 goals__** -- Use the distance formula to determine lengths on a coordinate plane, and, use the Midpoint Formula to find the midpoint of a line segment on the coordinate plane. **__9.6 Vocab--__** Distance Formula, midpoint, and Midpoint Formula

**__9.6 notes--__** MIDPOINT OF A LINE:(middle of the line) __ (x1+x2, y1+y2) __ ....2...........2 x and y are the coordinates of the line (4,1) (6,2) 4-6=-2/2=-1  1-2=-1/2=-.5  (-1,-.5)   __distance formula-__ (how long the line is) (X2-X1)^2+(y2-y1)^2, then the square root of that number.

**__9.7 goals-__** Identify corresponding parts and find missing measures of similar triangles, and solve problems involving indirect measurement using similar triangles. **__9.7 Vocab-__** similar triangles and indirect triangles **__9.7 Notes-__** similar-alike but not exactly the same (almost everything in common) same angle measurements sum of angles in a triangle-180 triangles exactly the same, the are congruent "goes with"=simila r                              __sine, cosine, tangent__ -are all trigonmetric ratios. -(sin cos tan buttons) -only work with right angles -need at least 2 pieces of info (other than right angle) to be able to solve **SohCahToa** - is used to determine... and stands for: **sine** = __measure of leg opposite of angle A__ measure of hypottanuse The **sine** of an angle is always the ratio of the (opposite side)/(hypotenuse).