31kanash

THE BEGINNING STEPS TO LEARNING GEOMETRY!

pudding.jpg
pudding.jpg

The Big Jump to the Beginning of Geometry
Point- Has no demensions.
Lines- Has one demension, it measures length, and it goes on forever.
Planes- Has two demensions, it measures length and width. Has to have at least three point to be a plane.
Points, lines, planes are considered undefined terms
Colinear- A single line that contains two points.
Coplanar- A plane that contains at least three points.
Segment- a line that has two endpoints.
Endpoints- Are two points that end a segment from going on forever like a line.
Ray- Is a part of a line with an endpoint on one end and the other end going on infinitely.
Angle- Has two rays connecting at a common end point.
Vertex of the angle- the common end point of an angle. Where two rays connect at a common endpoint.
Sides of an angle- The two rays that make up the angle.
Interior- The inside an angle.
Exterior- The outside of an angle.
Intersect- A figure that had one or more points in common.
Intersection- A group of points that they have in common.
Postulates- fundamental geometrical ideas.
The intersction of two lines is a point.
The intersection of two planes is a line.
Through any two points there is exactly one line.
Through any three noncollinear points there is exactly one plane.
If two points are ina plane, then the line containing them is in plane.

hippo.jpg
hippo.jpg


The Wonders of Measuring Length
Number line- A line that is set up to correspond with real numbers.
Coordinate of a point- A real number on a number line.
Length of AB- Finding the measures of points A and B on a number line.
Length- Is the measure of two points so the measurement of segment AB.
Segment congruence postuate- If you have two segments with the same length, the segments are considered congruent.
Segment addition postulate- Adding two segments together.

plato.jpg
plato.jpg


Angles! Angles! Angles! And How to Measure them
Degree
- Is the most common unit of angle measurement.
Measure of an angle- The vertex is placed at the center of a half of a circle between 0° and 180°.
Angle congruence postulate- Two angles that have the same angle measurement.
Complementry angles- Two angles add up to be 90°.
Complement- The other angle that adds together with another angle to measure 90°.
Supplementry angles- Two angles that add up to be 180°.
Supplement- The other angle that adds together with another angle to measure 180°.
Linear pair- An endpoint of a ray falls on a line to form two angles that will add up to be 180°.
Linear pair property- Two angles that create a linear pair is a supplementry angle.
Right angle- An angle that measures 90°.
Acute angle- An angle that measures less than 90°.
Obtuse angle- An angle that measure more than 90° and less 180°.

pottery.jpg
pottery.jpg


Paper Folding, Geometric Style
Constructions
- Something created under certain rules and is considered mathamatically precise.
Perpendicular line- Two lines that intersect to form a right angle.
Parallel lines- Two coplaner lines that never intersect. Paralle lines go on forever without touching.
Conjecture- A statement that you believe to be true. It is an "educated guess", based upon observation.
Segment bisector- A line in which divides a segment into two congruent parts.
Midpoint- The bisector that intersects the segment. It is located the exact middle if the segment.
Perpendicuar bisector- A line that divides a segment into two congruent parts. Where the line intersects the segment forms a right angle.
Angle bisector- A line or ray divides and angle into two congruent angles.


pumpkin.JPG
pumpkin.JPG

Special Triangles and their Points
Inscribed circle
- A circle within a triangle that touches all three sides of the triangle.
Circumscribed circle- A circle surrounding a triangle containing all three vertices.
Concurrent- Three or more lines interecting at a single point.
Incenter- Is the center of an inscribed circle. To find the center of the inscribed circle you find the angle bisector of each angle in the triangle.
Circumcenter- Is the center of a circumscribed circle. To find the center of a circumscribed circle you find the perpendicular bisector of each side of the triangle.
Inscribed and Circumscibed circle examples

whale.jpg
whale.jpg


The Motions of Geometry

Rigid transformation
- A figure is transformed and the shape and size of the figure does not change.
Preimage- The image before it is tranformed.
Image- The shape that was transformed from the preimage.
Translation- A figure transforms across a straight line. All points and line move the same direction and distance across the line.
Reflection- Is a line is like a mirror and a figure flippes across it.
Rotation- is a figure is moved at the same angle measurement. The figure is rotated from the center of rotation.

frog.jpg
frog.jpg


The Motions of Geometry using the Coordinate Plane
Horizonal Translation- H(x,y)=(x+0, y)
Vertical Translation- V(x,y)=(x,y+0)
Reflection across the X-axis- M(x,y)=(x,y-0)
Reflection across the Y-axis- N(x,y)=(x-0,y)
180° Rotation- (x,y)=(x+0,y+0) or (x-0,y-0)
Examples of transformation on a coodinate plane