Geometry Essentials of Geometry
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What is a point?
A point. It has no dimesnsion and is just a dot.
What is a line?
A one dimesioned figure that goes on forever. There is only one line no matter how many points are shown on the line. A line is named by the points on it.
What is a plane
A plane is a two dimesioned figure that extends without end in both directions. Planes can be name by three points that are not on the smae line.
What are collinear points?
Points that are on the same line
What are coplanar points?
Points that are on the same plane.
What is a line segment?
A line that contains enpoint and does not go on forever.
What is a ray?
A ray is a line with one endpoint, and one end goes on forever, like the suns rays.
What are opposite rays?
Rays that are on the same line and share and endpoint. For example, if C is between point A and B on a line, ray CA is the opposite ray of CB
What is an intersection?
The points that something shares. This can be a line, point, plane, multiple points, etc.
Will two planes always intersect at a line?
Remember to draw every possible thing you can in order to visualize!
If B is bwtween A and C what + what = AC?
What is segment addition?
It is adding two segments together to become a larger segment, like AB+BC=AC if B is between A and C on the same line.
What does congruent mean?
Equal to. It does not deal with measurements.
What is a midpoint?
A point on a segment that divides the line segment into two congruent segments.
What is a segment bisector?
Anything that intersects a line segment at the midpoint, wheter it be a ray, line, ect. It bisects the segment
What is the midpoint formula?
- The mid point formula is (average the x's, average the y's).
- There are other formulas. but they cannot be written, so if you prefer a different version, look back in your notes!
What is the distance formula used for?
Find the distance or length between segments
What is the distance formula?
- You can say:
- d2=(subtract the x's)2+(subtract the y's)2
- d= the square root of (x-x)2+(y-y)2
- Write it out!
- Count the boxes on a coordinate question if you can!
What is an angle?
Two rays that sare an endpoint.
What is the vertex of an angle?
The point where the two rays intersect.
What are the five tiypes of angles and what classify them?
- 0o<m<90o is an acute angle
- m=90o is a right angle
- 90o<m<180o is an obtuse angle
- m=180o is a straight angle
- 180o <m<360o is a reflexive angle
What is the Angle addition postulate?
Adding two touching angles that share a ray. m<RSP+m<PST=m<RST if SP is in between rays SR and ST.
What is an angle bisector?
A ray that divides an andle into two angles that are congruent.
What are complementary angles?
Two angles that add to 90 degrees, whether they are adjacent/touching or not.
What are supplemntary angles?
Two angles that add to 180 degrees whether they are adjacent/touching or not.
What is a linear pair?
A pair of supplementary angles that form a straight line. They must be adjacent/next to each other.
What do you know about vertical angles?
They are always congruent. Vertical angles are opposite angles of two intersecting lines.
What is a polygon?
A closed figure. It is formed by three or more line segments. Each side intersects exactly two sides, so that no sides share a common endpoint and become colinear.
What is the vertex of a polygon?
The endpoint of a side. The vertices determine what the name of the polygon is, since they are named in order around the shape.
What is the difference between a convex polygon and a concave polygon?
A convex polygon has sides that stick out, and a concave polygon has sides that go in.
What is important about regular polygons?
- They're sides are congruent.
- They're angles are congruent.
- It is a convex polygon
What is Pythagorean Theorem?
What is the converse of pythagorean's theorem?
- When you are given the lengths and are asked what king of triangle it is, think __.
- If it is =, it is a right trianlge.
- If it is >, then it is an acute trianlge.
- If it is <, then it is an obtuse trianlge
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