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Parallelograms and concurrency
parallelorgram and other shape properties, and concurrency properties!
29
Mathematics
10th Grade
01/27/2010

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Term
Centroid
Definition
name: Medians, sig.: divides 2:1, location: acute: inside, right: inside, obtuse: inside
Term
Incenter
Definition
name: Angle Bisectors, sig.: equidistant from sides, location: acute: inside, right: inside, obtuse: inside
Term
Circumcenter
Definition
name: perpendicular bisectors of sides. sig: equidistant from vertices, location: acute: inside, right: on midpoint of hypotenuse, obtuse: outside
Term
Orthocenter
Definition
name: Altitudes, locatioon: acute: inside, right: at vertex of right angle, obtuse: outside
Term
30 60 90 and 45 rules
Definition
short x 2 = hyp, short x root3 = medium, and for 45 short x root2=hyp
Term
Prove it's a kite:
Definition
either 2 sets of consecutives sides are congruent (but not all), OR one of the diagnols is a perpendicular bisector of the other
Term
prove it is a isosc. trapazoid:
Definition
either only one set is parallel and the other is congruent, OR only one set is parallel and one of the consecutive angles is congruent, OR one set of sides parallel and diagnals congruent
Term
Prove it's a rectangle:
Definition
ALL right angles, OR paralellogram with one right angle OR it is a parallelogram with the diagnals congruent
Term
Prove it's a rhombus:
Definition
either diagnals perpendicular bisect eachother, OR its a parallelogram with a set of consecutive sides congruent, OR its a parallelogram with a diagnol bisecting two angles
Term
Properties of Parallelogram
Definition
opposite sides are parallel, opposite sides are congruent, opposite angles are congrnent, diagnals bisect eachother, any pair of consecutive angles are supplimentary
Term
Properties of Kites
Definition
two disjoing pairs of consecutive sides congruent, diagnals are perpendicular, one diagnal perpendicular bisects the other, one diagnol bisects a pair of opposite angles, one pair of opposite angles are congruent
Term
Properties of Rhombuses
Definition
all properties of parallelogram, all properties of kites (half facts become full), all sides are congruent (equilateral), diagnols bisect the angles, diagnals divide rhombus into 4 congruent right triangles
Term
Properties of Squares:
Definition
all properties of rectangle, and rhombus apply, diagnols form 4 isosc. right triangles
Term
Properties of Isosc. Trapezoids:
Definition
Legs are congruent, bases are parallel, lower base angles and upper base angles congruent, diagnals congruent, lower base angle supp. upper base angle
Term
Properties of Rectangles:
Definition
all properties of parallelogram, all angles are right, diagnals are congruent
Term
Prove it's a parallelogram:
Definition
both sets of opposite sides parallel,OR both sets of opposite sides parallel, OR one set of opposite sides conruent and parallel, OR both sets of opposite angles congruent, OR diagnals bisect eachother
Term
Indirect Proof
Definition
list 2 different conclusions, (way it's written and opposite.) then assume the opposite, work through the proof, and get to concluding the opposite of a given, so you prove it isn't true.
Term
Probability
Definition
write out sample space, find total number of possibilities, find number of destined outcomes and circle those that apply.
Term
converse of p --> q
Definition
q --> p
Term
inverse of p --> q
Definition
~p --> ~q
Term
contrapositive of p --> q
Definition
~q --> ~p
Term
90, 180, 270 rotation pairs
Definition
90 = (-b,a) 180=(-a,-b) 270 = (b,-a)
Term
If shapes are similar
Definition
sides are porportionate, ANGLES ARE THE SAME.
Term
sum of exterior angles
Definition
360 degrees
Term
sum of interior angles
Definition
180(n-2)
Term
total number of diagnals
Definition
n(n-3) /2
Term
distance formula
Definition
square root of: (x1-x2)^2 + (y2-y1)^2
Term
measure of third side of a triangle
Definition
always going to be more than the sum of the other two sides
Term
perpendicular bisector reasoning
Definition
if pb --> any point equidistant from endpoints, if 2 pts equidistant from endpts --> pb
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