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Transcript of Geometry Terms
geometric principles trace back to three simple terms.
Point, line, and plane.
These terms are the building blocks of all that is
categorized as Geometry. THE BASICS TABLE OF CONTENTS 1. The Basics
point: intersection, midpoint, bisector
line: ray, line segment, collinear
plane: coplanar, space
types of polygons
properties of all polygons
properties of regular polygons
three-twelve sided polygons A B AB or BA Definition The definition of chair is: A separate seat for one person. A statement that clarifies the meaning of a word
or phrase. However, it is impossible to define
point, line, and plane without using words or
phrases that themselves need definition. The
Basics Plane Line Point Intersection Midpoint Coplanar Space Ray Line Segment Collinear An exact position or location on a plane surface No size Represented by a dot and named with a capital letter A straight, continuous arrangement of infinitely many points Infinite length, but no thickness Named by giving the letter names of any two points on the line and placing the line symbol above it A flat surface that extends infinitey along its length and width No thickness Named by titling with a script capital letter A type of line that begins at one point, the endpoint, and extends infinitely in one direction. Two letters are needed to name a ray.
The first letter is the endpoint and the
second is any other point that the ray
passes through. A part of a line marked by two endpoints. One segment includes all the points
between the endpoints that are collinear
with the two points Named by stating the two endpoints
and placing a line symbol
above it On the same line A B Line Segment AB or BA Ray K C CK Points A and B are collinear
because they are on the
same line A point on a line segment that divides
it into two equal parts When a line cuts another line into two
equal parts it is called a bisector. The
bisector will cut the line at its midpoint The point where two or more lines meet or cross A B L M K AB intersects LM at K E F H I J J is the midpoint of HI EF bisects HI IJ = JH IJ + JH = HI Lying on the same plane A B Point A and point B are coplanar A boudless three dimensional set
of all points Can contain both lines and planes ANGLES An angle is fomrd by two lines or rays diverging from a common point (vertex) The interior of an angle is the space in the 'jaws' of the angle extending out to infinity. The vertex is the common point at which the two lines or rays are joined. The sides of the angle are the two lines or rays that form the angle. A B C Vertex interior angle TYPES OF ANGLES Name Measure Right Obtuse Acute 90 90-180 0-90 Example Complementary Angle: two angles whose measurements have a sum of 90 Supplementary Angel: two angles whose measurements have a sum of 180 Linear angles: a pair of angles who are adjacent and whose measurements have a sum of 180 Pair of Vertical Angles: a pair of non - adjacent angles formed by two intersecting lines (degrees) Complementary: 45 45 45 + 45 = 90 Supplementary: 45 135 + 45 = 180 135 Pair of Vertical Angles: 1 2 1 = 2 Linear Angles 90 90 90 + 90 = 180 Definition:
A number of coplanar line segments, each
connected end to end to form a closed figure. polygons are one of the most all-encompasing
shapes in geometry NAME # OF SIDES triangle quadrilateral pentagon hexagon heptagon octogon nonagon decagon dodecagon undecagon 3 4 5 6 7 8 9 10 11 12 NAMED POLYGONS TYPES OF POLYGONS Regular: a polygon with all sides and interior angles the same. Regular polygons are always convex. Irregular: each side may be a different
length, each angle may be a different measure. The opposite of a regular polygon Convex: all interior angles less than 180°,and all vertices point away from the interior. The opposite of concave. Concave: one or more interior angles greater than 180°. Some vertices push towards the interior of the polygon. The opposite of convex. PROPERTIES OF ALL POLYGONS Interior Angles: angles at each vertex on the inside of the polygon. Exterior Angles: The angle on the outside of a polygon between a side and the extended adjacent side Diagonals: The diagonals of a polygon are lines linking any two non-adjacent vertices Area and Perimeter Interior Angle Diagonal Exterior Angle 45 PROPERTIES OF REGULAR POLYGONS Apothem (inradius): a line from the center to the midpoint of a side. This is also the inradius - the radius of the incircle Radius: a line from the center to any vertex. It is also the radius of the circumcircle of the polygon Incircle:the largest circle that will fit inside a regular polygon. Its radius is the apothem of the polygon Circumcircle: The circle that passes through all the vertices of a regular polygon. Its radius is the radius of the polygon Apothem Radius Incircle Circumcircle POLYGONS STEP THREE FINISH MIDPOINT FORMULA Between two points X + X , Y + Y
2 2 1 2 2 1 ( ( Example A B C (9,8) (X,Y) (2,6) 1. Plug the numbers into the formula 6+8 , 2+9
2 2 STEP ONE STEP TWO 2. combine like terms 14 11 2 , 2 3. Divide 2 , 2 14 11 7, 5.5 MIDPOINT= (7, 5.5) This has been a presentation by Kate Cellucci Thank you for watching! Geometry Challenge #2 Complete