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point of concurrency for perpendicular bisectors

circumcenter

point of concurrency for angle bisectors

incenter

point of concurrency for medians

centriod

point of concurrency for altitudes

orthocenter

angle bisector

a ray that divides an angle into 2 congruent parts

median

a segment whose endpoints are a vertex of a triangle and the midpoint of the opposite side

altitude

a perpendicular segment from the vertex to the opposite side

concurrent lines

three or more lines that intersect at the same point

perpendicular bisector

a segment line ray or plane that is perpendicular to a segment at it's midpoint

quadrilateral

a four-sided figure

parallelogram

a quadrilateral with two pairs of opposite sides congruent

rectangle

a parallelogram with four right angles

rhombus

a parallelogram with four sides congruent

square

a parallelogram with four right angles and four sides congruent

kite

a quadrilateral with adjacent sides congruent and no opposite sids congruent

trapezoid

a quadrilateral with one pair of parallel sides

isosceles trapezoid

a trapezoid whose non-parallel sides are congruent

consecutive angles

angles that share a side

consecutive sides

sides that share a vertex and are next to each other

diagonal

a line connecting two nonconsecutive vertices of a polygon

base angles (of a trapezoid)

angles that share a base

midsegment

a segment connecting the midpoints of two sides

point of concurrency

the point at which three or more lines intersect

perpendicular bisector of a triangle

a line that cuts a triangle directly in half

negation

statement with the opposite truth value

conditional

an if... then statement

inverse

negates both parts of a conditional

contrapositive

negates and switches the parts of a conditional

equivalent statements

statements with the same truth value

indirect reasoning

reasoning in which all possibilities are considered and all but one are proved false

sss postulate

proves if triangles have three congruent sides, they are congruent

sas postulate

proves if two sides and the angle between them are congruent in a pair of triangles, the triangles are congruent

asa postulate

proves if two angles and the side they share are congruent in a pair of congruent triangles, the triangles are congruent

aas

proves if two angles and a non-included side are congruent in a pair of triangles, the triangles are congruent

CPCTC

corresponding parts of congruent triangles are congruent

isosceles triangle

a triangle with two congruent sides

corollary

a statement following a theorem

transversal

a line that intersects two coplanar lines

alternate interior angles

nonadjacent angles that lie on opposite sides of a transversal

same side (consecutive) interior angles

angles that lie on the same side of a transversal

corresponding angles

angles that lie on the same side of a transversal in corresponding positions

alternate exterior angles

angles that lie outside of the lines on the opposite sides of a transversal

same side exterior angles

angles that lie outside of the lines on the same side of a transversal

linear pair

supplementary, adjacent angles

vertical angles

angles that are made with intersecting opposite rays

equilateral (also equiangular)

all sides congruent of a triangle

equiangular (also equilateral)

all angles congruent of a triangle

regular polygon

a polygon that is both equiangular and equilateral

p

symbol for the hypothesis of a conditional

q

symbol for the conclusion of a conditional

biconditional

if then only if statement (both conditional and converse are true of a statement)

deductive reasoning

reasoning logically to reach a conclusion

law of detachment

if the first part of a conditional is true, the second part is true

law of syllogism

if p then q, if q then r, if p then r

reflexive property

a congruent to b, b congruent to a

transitive property

a congruent to b, b congruent to c ,then, a congruent to c.

complementary

angles whose measures add up to 90

supplementary

angles whose measures add up to 180

plane

a flat two dimensional surface

line

a series of points extending in different directions without ending

point

a location represented by a dot on a graph

space

the set of all points, 3D

skew lines

lines that are noncoplanar and never intersect

parallel lines

coplanar lines that never intersect

line

planes intersect in exactly one...

point

lines intersect at exactly one..

angle

two rays with the same endpoint