Geometry Definitons

Geometry : the study of shapes and their spatial properties

Point : an exact location in space

endpoint : a point at the end of a line

line segment : part of a line w/two endpoints. or a line that stops at both ends

postulates 1-1 : there is exactly one (straight) line through any two points

postulates 1-2 : there is exactly one plane that contains any three non-collinear points

distance : the length between two points

measure : to determine how far apart two geometric objects are

sides : the two rays that form an angle

protractor postulate : for every angle there is an number between 0 to 180 degrees that is the measure of the angle in degrees. the angle's measure is then the absolute value of the difference of the numbers shown on the protractor where the sides of the angle intersect the protractor

perpendicular : when two lines intersect to form four right angles

angle addition postulates : the measure of any angle can be found by adding the measures of the smaller angles that are in it

segment bisector : a line, segment, or ray that passes through a midpoint of another segment

perpendicular bisector : a line, ray, or segment that passes through the midpoint of another segment and intersects the segment at a right angle

supplementary : when two angles add up to 180 degrees just like comp. angles, supp. angles do not have to be congruent or touching

congruent linear pair : the angles are congruent to each other and must add up to 180 degrees

vertical angles theorem : if two angles are vertical angles, then they are congruent

inductive reasoning : making conclusions based upon observations and patterns

conclusion : the second, or then, part of a conditional statement. the conclusion is the result of a hypothesis.

normal : p-qif i am at disneyland, then i am in CA

logic : the study of reason

deductive reasoning : when a conclusion is drawn from facts. typically conclusions are drawn from general statements about something more specific

symmetric property of equality : m of angle = 90 degrees or 90 degrees of m of angle

transitive property of equality : a+4=10/ 10=b+4/ a+4=b+4

division property of equality : 3b=18, 3b/3=18/3

distributive property : anything to do with parenthesis

same angle supplements theorem : if two angles are supplementary to the same angle, then the angles are congruent

same angle complements theorem : if two angles are complementary to the same angle then the angles are congruent

transversals : a line that intersects two distinct lines. These two lines may or may not be parallel

corresponding angles : to angles that are in the same place w/respect to the transversal but on different lines

alt. int. angles therom : if two parallel lines are cut by a transversal, then the alt. int. angles are congruent

alt. ext. angles therom : it two parallel lines are cut by a transversal, then the alt. ext. angles are congruent

converse of the same side int. angles therom : if two lines are cut by a transversal, and the consecutive int. angles are supplementary, then the lines are parallel

parallel lines property : if l is parallel to m, and m is parallel to n, then l is parallel to n.

slope-int : y=mx+b

parallel lines slope : have same slop, byt different y-int

interior angles : the angles inside of a closed figure with straight sides

vertex : the point where the sides of a polygon meet

isosceles triangles : two congruent sides

equilateral triangles : is a triangle with equal sides

ext. angle thrm : the sum of the measure of remote int. angles= the measure of the exterior angle

remote interior angles : the two angles in a triangle that are not adjacent to the indicated enterior angle

symmetirc property of congruency : it two shapes are congruent, the statement can be written with either shape on either side of the congruent signs

SSS : if three sides in one triangle are congruent to three sides in another, then the triangle are congruent

hypotenuse leg thrm : if the hypotenyuse and leg in one right triangle are congruent to the hypotenuse and leg in another right triangle then the two triangles are congruent

AAA : implied that all the angles are congruent however that doesnt mean the triangles are congruent

and the anlges between the base and the congruetn sides are called : base angles

the angle made by the two legs of the iso. triangles is : the vertex angle

by definiton all sides in an equilateral triangle have : exactly the same length therefore every equilateral triangle is also an isosceles triangle

equilateral triangle thrm : all equilateral triangles are also equiangular. also all equiangular triangles are equilateral

perpendicular bis. thrm converse : if a point is equidistance from the endpoints of a segment, then the point is on the perpendicular bis of a segment

point of concurrency : when two or more lines intersect @ same point

altitudes concurrency : concurrent at the orthocenter

angle bis. concurrency : concurrent at the incentercenter of the inscribed (inside triangle)equidistance from sides of triangle

median : the line segment that joins a vertex and the midpt of the opp. side

centroid : the pt. of concurrency for the medians of a triangle

thrm. 5-9 converse : if one angle in a triangle is larger than another angle in a triangle

triangle inequality thrm : the sum of the lengths of any twos sides of a triangle, must be greater than the length of the third

regular polygon : when a polygon is equilateral and equilangular

ext. angle sum thrm : the sum of the ext. angles of any polygon is 360*

parallelogram diagonals thrm : if a quadrilateral is a parallelogram then the diagonals bisect each other

opp. sids thrm converse : if the opp. sides of a quadrilateral are congruent, then the figure is a paralleogram

rectangle thrm : a quadrilateral is a rectangle if and only if it has 4 right angles

rhombus thrm : a quadrilateral is a rhombus if and only if it has four congruent sides

thrm 6-17 : the base angles of an iso. trap are congruent

thrm 6-17 onverse : it a trapezoid has congruetn base angles then it is an iso. trap

midsgmt. of a trapezoid. : a line seg. that connects the midpts of the non-parallel sides

midsgt thrm : the length of the midsgt of a trap is the average of the length of the bases or EF=AB+CD/2

ratio : a way to compare two numbers can be writter: a/b, a:b, and a to b

proportions : when two ratios are set equal to each other

All squares are similar : ...

Scale factor : in similar polygons, the ratio of one side of a polygon to the corresponding side of the other

Triangle Proportional Thrm : If a line parallel to ne side of a trianlge intersects the other two sides, then it divides those sides proportionally

Triangle Prop. Thrm Conv. : IF a line divides two sides of a triangle proportionally, then it is parallel to the third side

def. of betweeness : collinear and AB+BC=AC, A-B-C

If the inverse is false : then the converse must also be false

Complementary angles measure 45* : sometimes

if line XY is congruent to line CD, then line XY is equal to line CD : never ( due to the notation which you cannot see on quizlet)

any 4 distinct points are coplanar : somtimes (3 must be collinear)

The sum of the ext. angles of a triangle are 180 : never, the sum is 360

k : dialation factor

enlargment : k>1