ABC’S OF GEOMETRY
By Parker Davis January 2, 2012
AA similarity when two triangles have corresponding angles that are congruent as shown below, the triangles are similar  AAS if two angles and the nonincluded side one triangle are congruent to two angles and the nonincluded angle of another triangle, then these two triangles are congruent  Acute angle an angle with an angle measure less than 90°  Acute triangle a triangle where all three internal angles are acute  Alt. exterior angles alternate exterior angles are created where a transversal crosses two (usually parallel) lines. each pair of these angles is outside the parallel lines, and on opposite sides of the transversal.  Alt. interior angles alternate interior angles are created where a transversal crosses two (usually parallel) lines. each pair of these angles are inside the parallel lines, and on opposite sides of the transversal  Altitude a line that is perpendicular to the base and goes through the opposite vertex  Angle bisector a line that equally spits an angle into two parts  ASA if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then these two triangles are congruent  oBtuse triangle a triangle that has an angle with a measure greater than 90°  Centroid the point of congruency of three medians in a triangle  Circumcenter point of congruency of three perpendicular bisectors  Collinear points the points lying on the same line are called collinear points  Complementary angles two angles are complementary if they add up to 90°  Concave polygon a polygon that has one or more interior angles greater than 180°  Conditional statements a conditional is a compound statement formed by combining two sentences (or facts) using the words “if ... then” IF…THEN IF…THEN

Congruent two figures are congruent if they have...
...Geometry Conjectures
Chapter 2
C1 Linear Pair Conjecture  If two angles form a linear pair, then the measures of the angles add up to 180°.
C2 Vertical Angles Conjecture  If two angles are vertical angles, then they are congruent (have equal measures).
C3a Corresponding Angles Conjecture If two parallel lines are cut by a transversal, then corresponding angles are congruent.
C3b Alternate Interior Angles Conjecture If two parallel lines are cut by a transversal, then alternate interior angles are congruent.
C3c Alternate Exterior Angles Conjecture If two parallel lines are cut by a transversal, then alternate exterior angles are congruent.
C3 Parallel Lines Conjecture  If two parallel lines are cut by a transversal, then corresponding angles are congruent, alternate interior angles are congruent, and alternate exterior angles are congruent.
C4 Converse of the Parallel Lines Conjecture  If two lines are cut by a transversal to form pairs of congruent corresponding angles, congruent alternate interior angles, or congruent alternate exterior angles, then the lines are parallel.
Chapter 3
C5 Perpendicular Bisector Conjecture  If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints.
C6 Converse of the Perpendicular Bisector Conjecture  If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.
C7 Shortest Distance Conjecture  The...
...Geometry Definitions, Postulates and Theorems
Definitions Name Complementary Angles Supplementary Angles Theorem Vertical Angles Transversal Corresponding angles Sameside interior angles Alternate interior angles Congruent triangles Similar triangles Angle bisector Segment bisector Legs of an isosceles triangle Base of an isosceles triangle Equiangular Perpendicular bisector Altitude
Definition Two angles whose measures have a sum of 90o Two angles whose measures have a sum of 180o A statement that can be proven Two angles formed by intersecting lines and facing in the opposite direction A line that intersects two lines in the same plane at different points Pairs of angles formed by two lines and a transversal that make an F pattern Pairs of angles formed by two lines and a transversal that make a C pattern Pairs of angles formed by two lines and a transversal that make a Z pattern Triangles in which corresponding parts (sides and angles) are equal in measure Triangles in which corresponding angles are equal in measure and corresponding sides are in proportion (ratios equal) A ray that begins at the vertex of an angle and divides the angle into two angles of equal measure A ray, line or segment that divides a segment into two parts of equal measure The sides of equal measure in an isosceles triangle The third side of an isosceles triangle Having angles that are all equal in measure A line that bisects a segment and is perpendicular to it A segment from...
...Geometry was throughly organized in about 300 B.C, when the Greek mathematician, Euclid gathered what was known at the time; added original book of his ownand arranged 465 propositions into 13 books called Elements.
Geometry is the mathematics of space and shape, which is the basis of all things that exist. Understanding geometry is necessary step by understanding how the things in our world exist. The applications of geometry in real life are not always evident to teenagers, but the reality is geometry infiltratesevery facet of our daily living.
Geometry was recognized to be not just for mathematicians. Anyone can benefit from the basic learning of geometry, which is to follow the lines reasoning. Geometry is one of the oldest sciences and is corcerned with questions of shape, size and relative position of figures and with properties of space.
Geometry is considered an important field pf study because of its applications in daily life.
Geometry is mainly divided in to two which is plane geometry and solid geometry. Plane geometry is about all kinds of two dimensional shapes such as lines, circles, and triangles. While Solid geometry is about all kinds of three dimensional shapes like polygons, prisms, pyramids, sphere and cylinder.
Now, let’s move on its...
...cm".
A square has an area of sixteen square centimeters. What is the length of each of its sides?
The formula for the area A of a square with sidelength s is:
A = s2
They gave me the area, so I'll plug this value into the area formula, and see where this leads:
16 = s2
4 = s
After rereading the exercise to find the correct units, my answer is:
The length of each side is 4 centimeters.
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Most geometry word problems are a bit more involved than the example above. For most exercises, you will be given at least two pieces of information, such as a statement about a square's perimeter and then a question about its area. To find the solution, you will need to know the equations related to the various pieces of information; you will then probably solve one of the equations for a useful bit of new information, and then plug the result into another of the equations.
In other words, geometry word problems often aren't simple onestep exercises like the one shown above. But if you take all the information that you've been given, write down any applicable formulas, try to find ways to relate the various pieces, and see where this leads, then you'll almost always end up with a valid answer.
A cube has a surface area of fiftyfour square centimeters. What is the volume of the cube?
The formula for the volume V of a cube with edgelength e...
...Collaboration Component Form
Please complete this fourpart guide, and
submit for the collaboration component.
Make sure to save this file with the module number (no periods)
and your name. Thank you.
1. Collaboration lesson/task description: Describe the lesson or task you completed collaboratively
in a paragraph consisting of five or more sentences.
or more sentence , tons of details, excellent grammar, punctuation and spelling
2. Peer and selfevaluation: Rate each member of the team, including yourself, according to each of
the performance criterion below.
3 = above average
2 = average
1 = below average
f you attended a live
Listened to others
Showed respect for others' opinions
Completed assigned duties
Participated in discussions
Attended meetings
Stayed on task
Offered relevant information
Completed work adequately
Completed work on time (with no
reminders)
Offered appropriate feedback when
necessary
Created on Friday, November 22, 2013
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Student 8
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Your name
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3. Selfreflection: Respond to the
to
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sentences each, tons of details, excellent grammar, punctuation and
Explain what you enjoyed most about working with others on this lesson/task.
Explain how your team dealt with conflict.
Explain how you feel others felt about your...
...“Bringing it all Together: The Geometry of Golf”
Golf in Geometry?? No Way!
Geometry In The Game of Golf
For hundreds of years, golf has been an extremely popular and growing sport all around the world. Looking where golf is now, it is growing rapidly from the young to the elder population. The first round of gold was first played in the 15th century off the coast of Scotland, but it did not start to be played until around 1755. The standard rules of golf were written by a group of Edinburgh golfers. Today, people of the US, Scotland, and England, have been drawn to the game because it is fun, challenging, and hardly any athletic ability at all is required for amateurs. In breaking down the game, geometry plays a major role, and can influence a players score dramatically. Geometry plays a key role and influences aspects such as the ball, course, or golf swing.
First Geometry is important in the design of the golf ball. It is crucial that the golf ball is not a perfect sphere, but as close to a sphere as possible. Before man could create the perfect golf ball, the main idea was to create a close to perfect sphere without any implications that would mess up the distance and direction of the ball. If the ball is not a perfect sphere, without any davits, the ball would not get any spin on it and would go the wrong direction.
Furthermore geometry is used in...
... 9. Dodecagon
10. Tetradecagon
F. Circles
Introduction
"Geometry," meaning "measuring the earth," is the branch of math that has to do with spatial relationships. In other words, geometry is a type of math used to measure things that are impossible to measure with devices. For example, no one has been able take a tape measure around the earth, yet we are pretty confident that the circumference of the planet at the equator is 40,075.036 kilometres (24,901.473 miles) . How do we know that? The first known case of calculating the distance around the earth was done by Eratosthenes around 240 BCE. What tools do you think current scientists might use to measure the size of planets? The answer is geometry.
However, geometry is more than measuring the size of objects. If you were to ask someone who had taken geometry in high school what it is that s/he remembers, the answer would most likely be "proofs." (If you were to ask him/her what it is that s/he liked the least, the answer would probably be "proofs.") A study of Geometry does not have to include proofs. Proofs are not unique to Geometry. Proofs could have been done in Algebra or delayed until Calculus. The reason that High School Geometry almost always spends a lot of time with proofs is that the first great Geometry textbook, "The Elements," was written exclusively with proofs....
...Line Segment
1.) Mark a point R that will be one end of the new line
2.) Place the compass point on one end of the line
3.) Adjust the compass width to the other end of the line
4.) Without changing the compass width, move the compass to point R
5.) Draw an arc near where the end of the new line will be
6.) Pick a point S on the arc to be the endpoint of the new line
7.) Draw a straight line between R and S
Copy an Angle
1.) Mark a point P to be the vertex of the new angle
2.) Draw a ray PQ in any direction and any length. This will be one side of the new angle
3.) Set the compass point on A and adjust it to any convenient width
4.) Draw an arc across both sides of the angle, creating points J and K
5.) Move the compass to P and draw a similar arc, crossing PQ at M
6.) Set the compass on K and set its width to J
7.) Move the compass to M and draw an arc crossing the first, creating point L
8.) Draw a ray PR from P through L
Perpendicular Bisector
1.) Place the compass point on one end of the line
2.) Adjust the compass to just over half the line length
3.) Without adjusting the compass width, draw an arc on each side of the line
4.) Without changing the compass width, repeat for the other end of the line
5.) Draw a straight line between the two arc intersections
Angle Bisector
1.) Place the compass point on the angle's vertex
2.) Set the compass to any convenient width...