PLANE GEOMETRY Flashcards
WHAT DO YOU CALL THE COMMON ENDPOINT OF THE TWO RAYS IN AN ANGLE
VERTEX!
DEFINITION OF OBTUSE ANGLE
GREATER THAN 90 BUT LESS THAN 180,
180 DEGREE ANGLE IS CALLED A STRAIGHT ANGLE.
WHAT DO YOU CALL IF AN ANGLE HAS A MEASUREMENT OF GREATER THAN 180 BUT LESS THAN 360
REFLEX ANGLE
ANGLE WITH 360 DEGREE
FULL ANGLE.
BESIDES RADIAN AND DEGREE, WHAT OTHER UNITS ARE THERE TO MEASURE ANGLES,
ANDDDDD
WHAT IS THEIR CONVERSION TO DEGREE.
1 DEGREE = ______????
GON/GRADIAN= ONE FULL CYCLE IS 400;
1 DEGREE = 1.1111GON
MIL= 1 FULL ROATION IS 6400 1DEGREE = 17.78 MILS
WHEN TWO ANGLES HAVE THE SAME MAGNITUDE, THEY ARE CONSIDERED?
CONGRUENT
WHEN TWO ANGLE THAT START AND END AT THE SAME POINT AND HAVE MAGNITUDES THAT DIFFER BY A MULTIPLE OF 360 DEGREES
COTERMINAL
Coterminal angles: are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side. For example, the angles 30°, –330° and 390° are all coterminal
AN ACUTE ANGLE THAT CAN BE OBTAINED BY CONTINUALLY SUBTRACTING 180 DEGREE FROM A REFLEX ANGLE
REFERENCE ANGLE
COMPLEMENTARY ANGLE MEANS
2 ANGLE WHEN ADDED EQUALS 90
SUPPLEMENTARY ANGLE MEANS
2 ANGLES WHEN ADDED EQUALS 180
EXPLEMENTARY ANGLE MEANS
2 ANGLES WHEN ADDED EQUALS 360
what do you call a polygon where it’s sides are all equal in length, and what do you call its counterpart.
REGULAR, and IRREGULAR POLYGON
FORMULA FOR THE INTERIOR ANGLE & exterior angle OF A REGULAR POLYGON
Σ Interiorθ = (n-2) 180
Σ Exteriorθ = 360
Interiorθ = [(n-2) 180]/n
where n= the number of sides of the polygon
FORMULA FOR The number of diagonals in a POLYGON
Number of diagonals =n/2 (n-3)
FORMULA FOR The perimeter and area of a regular! POLYGON
Area= 1/4 na^2 cot(180/n) n= number of sides a= length of one side
perimeter= na
what do you call the line with a single point of intersection with a circle.
tangent line
what do you call the line with 2 points of intersection with a circle
secant line
a LINE WITH two endpoints within a circle that is does not cross the center,
CHORD
-if it does cross the center, then that would be called the diameter
what is an arc?
a part of the circumference of a circle (like a piece)
what is the difference between a central angle and an inscribed angle?
center angle has the central point of the circle as its vertex, inscribe angle is any other angle formed within the circle.``
formula for circle area and circumference
A= πr^2 C= 2πr = πd
formula for the sector length and its area- which is part of the circle circumference - arc - ( slice of pizza)
S =rθ
θ= angle of the arc in RADIAN!
Sector Area = As= 1/2 rs = 1/2 r^2 θ
a piece of a circle where it is cut by chord line
chord means?
CHORD line is a LINE WITH two endpoints within a circle that is does not cross the center,
this PIECE IS CALLED A SEGMENT!
FORMULA FOR THE AREA OF A SEGMENT
A= As - At
As= SECTOR AREA (slice of pizza) At= Triangular piece within the As
______ THEOREM SAYS THAT FOR THREE POINTS ABC OF A CIRCLE, IF THE LENGTH OF LINE AC IS EQUAL TO THE DIAMETER, THEN THE THREE POINTS FORMS A RIGHT TRIANGLE.
THALES THEOREM
WHEN TWO CHORDS INTERSECT THE LENGTHS OF THE DIVIDED SEGMENTS WHEN MULTIPLIED WILL BE EQUAL
SEGMENT AB=CD
CROSS CORD THEOREM
SECANT THEOREM FORMULA
2 SECANT LINE
FOR SECANT LINE AB & CD
A (A+B) = C (C+D)
SECANT TANGENT THEOREM
1 SECANT AND 1 TANGENT LINE
FOR SECANT LINE AB & TANGLEN LINE D
A(A+B)= D^2
FORMULA FOR THE AREA & perimeter OF A CIRCLE INSCRIBED! IN A regulat regular regular!!!! POLYGON
(in)
A=nr^2 tan(180/n)
n= number of sides
r= radius
Permiteer
P= 2nr tan(180/n)
FORMULA FOR THE AREA & perimeter OF A CIRCLE circumscribed! by A regulat regular regular!!!!
POLYGON
(out)
A= (nr^2)/2 sin (360/n)
P=2nr sin(180/n)
