GEOMETRY

//Area of a rectangle = Height x Width//
 * Areas of Polygon**

//Area of a triangle = 1/////2 x (b x h)// = = //Area of a Parallelogram// //= B x H// //Area of a Rhombus = 1/2(d1) x d2// //Area of a Circle - Circumference **[** **C = 2pi(r) or C = pi(d) ]**//

//- Area **[** **A = pi(r)squared ]**// //Area of a Trapezoid : A = 1/2(b1 + b2)h// TRAPEZOIDS
 * **Trapezoid**: A quadrilateral with exactly 1 pair of parallel sides.[[image:file:///C:/Users/Lan-Anh/AppData/Local/Temp/moz-screenshot.png]][[image:file:///C:/Users/Lan-Anh/AppData/Local/Temp/moz-screenshot-1.png]][[image:file:///C:/Users/Lan-Anh/AppData/Local/Temp/moz-screenshot-2.png]][[image:file:///C:/Users/Lan-Anh/AppData/Local/Temp/moz-screenshot-3.png]][[image:file:///C:/Users/Lan-Anh/AppData/Local/Temp/moz-screenshot-4.png]][[image:file:///C:/Users/Lan-Anh/AppData/Local/Temp/moz-screenshot-5.png]][[image:file:///C:/Users/Lan-Anh/AppData/Local/Temp/moz-screenshot-6.png]][[image:file:///C:/Users/Lan-Anh/AppData/Local/Temp/moz-screenshot-7.png]]


 * < I and < O are base angles.
 * < L and < N are base angles

=~ legs.
 * **Isosceles Trapezoid**: a trapezoid with
 * __//Theorems//__//**:**// If a trapezoid is Isosceles then the angles are =~
 * //__Theorems__**:**// If a base angles of a trapezoid is =~ then it is an Isosceles Trapezoid.


 * **Parallelogram:** a quadrilateral with both pairs of opposite sides parallel.
 * picture
 * __//Theorems://__
 * 1) If a quadrilateral is a parallelogram, then it's opposite **sides** are congruent
 * 2) If a quadrilateral is a parallelogram, then it's opposite **angels** are congruent
 * 3) if a quadrilateral is a parallelogram, then it's consecutive angels are supplementary.
 * examples pictures of Theorem 1, 2, 3
 * 1) If a quadrilateral is a parallelogram, then it's diagonals bisect each other
 * example picture of theorem 4


 * **Polygons**
 * A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others.

>> || 3 || triangle || >> || 4 || quadrilateral || >> || 5 || pentagon || >> || 6 || hexagon || >> || 7 || heptagon || >> || 8 || octagon || >> || 9 || nonagon || >> || 10 || decagon || >> || 11 || hendecagon || >> || 12 || dodecagon ||
 * Chart...
 * Sides || Names ||


 * **Regular Polygon**
 * A regular polygon is a polygon whose sides are all the same length, and whose angles are all the same measure
 * pictures of regular pentagon, and irregular pentagon.

=Properties of Tangents=


 * Theorem**: If a line is a tangent to a circle, then it is perpendicular to the radius drawn at the point of tangency.




 * Theorem**: In a plane, if a line is perpendicular to a radius of a circle at its endpoint on the circle, then the line is tangent to the circle. [ Same example as above ]


 * Theorem**: If two segments from the same point outside a circle are tangent to the circle, then they are congruent.



=Arcs and Central Angles=

Arc Addition Postulate

The measure of an arc formed by two adjacent arcs is the sum of the measure of the two arcs. Arc Length In a circle, the ratio of the length of a given arc to the circumference is equal to the ratio of the measure of the arc to 360 degrees
 * Arc length is equal to 24/360 [times] 2pi (r).**



Parallel lines:

 * lines on the same plane & and do not intersect.

Skew Lines:
 * lines that are not parallel and do not intersect each other



Perpendicular Lines:
 * Lines that intersect each other at a 90 degree angle

- a line is perpendicular to a plane if it intersects the plane at a 90 degree angle**
 * - 2 planes are parallel if they don't intersect each other




 * Perpendicular Lines**

**Angles 1 + Angle 2 = 90 Degrees**
 * Theorems**
 * 1) All right angles are congruent
 * 2) If two lines are perpendicular, they intersect to form 4 right angles
 * 3) If 2 lines intersect to form congruent adjacent angles, then the lines are both perpendicular
 * 4) If 2 non-common sides of adjacent angles are perpendicular, then the angles are complementary

Angles formed by Transversal


 * Transversal:** A lines that intersects 2 or more coplaner lines at different paths



Alternate Interior Angles <4 & <6 <3 & <5 Alternate Exterior Angles <1 & <7 <2 & <8 Same Side Interior 4 & <5 <3 & <6 Corresponding Angles <1 & <5 <3 & <7 <2 & <6 <4 & <8

Parallel Lines and Transversal

If two lines are parallel and transversal intersect the 2 lines, then 1) Corresponding angles are congruent 2) Alternate Interior angles are congruent 3) Alternate Exterior Angles are congruent

How to Solve Proofs
sequence of justified conclusions used to prove the validity of an if-then statement.



Simplifying Square Roots
Square roots are written with a radical symbol. The radical symbol always indicates the nonnegative square root of a number. For example, radical sign 25 = 5 because 5 squared equals 25.


 * Finding Side Lengths**

To find side lengths or a triangle use this formula:

We use cosine, sine, and tangent to find sides of a ride angled triangle.




 * "Opposite" is opposite to the angle θ
 * "Adjacent" is adjacent (next to) to the angle θ
 * "Hypotenuse" is the long one


 * Sine Function: || **sin(//θ//) = Opposite / Hypotenuse** ||
 * Cosine Function: || **cos(//θ//) = Adjacent / Hypotenuse** ||
 * Tangent Function: || **tan(//θ//) = Opposite / Adjacent** ||

Example 1: what are the sine, cosine and tangent of 30° ?
The classic 30° triangle has a hypotenuse of length 2, an opposite side of length 1 and an adjacent side of √(3): Now we know the lengths, we can calculate the functions:
 * **Sine** || sin(30°) = 1 / 2 = 0.5 ||
 * **Cosine** || cos(30°) = 1.732 / 2 = 0.866 ||
 * **Tangent** || tan(30°) = 1 / 1.732 = 0.577 ||