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All Chapter 9 Notes:

NOTES: 9.1 **__Square Root:__** a number multiplied by itself Ex. 7x7=49 This is an example of a square root. Examples:5*5=25 5 is the square root 8*8=64 8 is the square root. 12*12=144 12 is the square root Numbers like 25, 49, 169, and 225 are perfect squares. They are perfect squares because they are squares if whole numbers. When a number is multiplied by itself, it is the same thing as that number to the 2nd power, or "Squared" **__Radical Sign:__** used to indicate the square roo t

9.2 An irrational number is a number that cannot be expressed as //a/b,// where //a// and //b// are integers and //b// does not equal 0. **__Real Numbers:__** a set of irrational numbers together make up real numbers **Examples :** 0.101001000100001... **Real Number Site:** [] **__Rational Number:__** any number that can be written as a fraction. 9.3 The vertex is the common endpoint of the rays forming an angle Right Angle: 90 degrees Acute Angle: Less than 90 degrees Straight Angle:180 degrees Obtuse angle: more than 90 and less than 180 degrees. Reflex Angle: More than 180 degrees

9.4 A line segment is part of a line containing two endpoints and all of the points between them. A triangle is a figure formed by three line segments that intersect only at their endpoints.

Vertices is the plural of vertex.

The sum of the measures of the angles of a triangle is 180 degrees.

All triangles have at least two acute angles. The third angle is either acute, obtuse, or right.

Congruent sides have the same length. A scalene triangle has NO congruent sides. Isosceles Triangle has two sides that are congruent. An equilateral triangle has ALL congruent sides. A right triangle has a right angle.

9.5 In a right triangle, the sides that are adjacent to the right angle are called the legs. The side opposite to the right angle is the hypotenuse. Hypotenuse= C a squared+b squared=c squared A and B are the sides (legs) that make up the right angle

They make up the right angle C is the Hypotenuse a2+b2=c2 = Pythagorean Thoerem 9. 5

The two lines that make up the right angle in a right triangle are called legs. The other side is called the hypotenuse.

9.6 To get the midpoint do (x1+x2 ) ( y1+y2) 2 2 The purpose of the midpoint formula is to find the exact middle of two points.

Distance formula=√(x2-x1)² + (y2-y1)²

The purpose of the distance formula is to find the distance from point A to point B.

9.7

Similar triangle are triangle that have the same shape but not necessarily the same size. If two triangle are similar, then the corresponding angles have the same measure, and the corresponding sides are proportional. Indirect measurement - Using the properties of similar triangles to find measurements that are difficult to measure directly.

Sine, Cosine, and Tangent are trigonometric ratios that describe the sides of a right triangle. You can find the sin, cos, and tan of a degree of a right triangle. SohCahToa= Sin=opposite/hypotenuse Cos= adjacent/hypotenuse Tan= opposite/adjacent Trigonometric ratios: the ratio between the lengths of 2 sides of a right traingle []

Formulas: Sin = opposite/hypotenuse Cos = adjacent/hypotenuse Tan = opposite/adjacen t

1.Label H,O,A 2.Write SOHCAHTOA and find which you are using. 3.Put In #s. 4.S/C/T=turn into a # 5.get x alone(answer)

10.1 Notes: [|__http://www.stixy.com/__] or [|__http://www.stixy.com/__]

In geometry, 2 lines that never intersect are parallel. When 2 parallel lines are intersected by a line, that line is called a transversal. They form 8 angles: Interior angles, which are inside the parallel lines, Exterior angles, which are outside the lines Alternate interior angles, which are on the opposite side of the transversal and are inside the lines, Alternate exterior lines, which are on the opposite side of the transversal and are outside the parallel lines Corresponding angles, which are in the same postion on the parallel lines and in relation to the transversal. When 2 lines intersect, they form opposite angles called vertical angles. When 2 angles have the same vertex, they are adjacent angles. If the sum of the 2 angles are 90 degrees. the angles are complentary.If the sum is 180 degrees, the angles are supplementary. Lines that intersect and form a right angle are perpendicular lines.

10.2 Notes: Congruet: Exactly the same Similar: Exactly same shape and angles but the sides are different

10.3 Translation: Rotation: Reflection:

10.4 Notes: Polygon: a figure with at least 3 sides that are connected and not curved Quadrilateral: 4 sided polygon Trapazoid: 4 sided and 2 sides are parallel. To find the area of trapazoid: 1/2h(a+b) Area has to be units squared. Parallelogram: 4 sided figure with 2 sets of parallel lines Formula: Area= b*h Rectangle: Area= b*h Square: Area= sides squared Rhombus: 4 sided closed figure, opposite sides parallel, and all sides are the same length 10.5

10.6 Notes: Sides Name Angle Measurement 3 Triangle 180 4 Quadrilateral 360 Rectangle 360 Square 360 Rhombus 360 Trapazoid 360 Parallelogram 360 5 Pentagon 540 6 Hexagon 720 7 Heptagon 900 8 Octagon 1080 9 Nonagon 1260 10 Decagon 1440 11 Hendecagon 1620 12 Dodecagon 1800 x Nona-gon 180(n-2)

10.6 and 10.7 []