postulate

a statement that is accepted as true without proof

plane

a flat surface that has no thickness

skew lines

noncoplaner lines that do not intersect and are not parallel

midpoint

a point that divides a segment into two congruent parts

adjacent angles

two coplanar angles with a common side, a common vertex, and no common interior points

complementary angles

two angles whose measure sum to 90 degrees

supplementary angles

two angles whose measure sum to 180 degrees

perpendicular bisector

a line, segment, or ray that is perpendicular to the segment at its midpoint, thereby bisecting the segment.

angle bisector

a ray that divides an angle into two congruent coplanar angles

converse

switches the hypothesis and conclusion of a conditional statement

biconditional

made when a conditional and its converse are true; connected with "if and only if"

law of detachment

if a conditional is true and its hypothesis is true, then its conclusion is true. (if p -> q is true and p is true then q is true)

law of syllogism

if p -> q and q -> r are true statements, then p -> r is a true statement

reflexive property

a=a

symmetric property

if a=b, then b=a

transitive property

if a=b and b=c, then a=c

triangle sum theorem

the sum of the measures of the angles of a triangle is 180

triangle exterior angle theorem

the measure of each exterior angle of a triangle equals the sum of the 2 remote interior angles

scalene triangle

no congruent sides

isosceles triangle

at least 2 congruent sides

equilateral triangle

3 congruent sides

acute triangle

3 acute angles

right triangle

1 right angle

obtuse triangle

1 obtuse angle

equiangular triangle

3 congruent angles

polygon

a closed plane figure with at least 3 sides that are segments

polygon angle sum theorem

(n-2)x180

polygon exterior angle theorem

the sum of the measure of the exterior angles of a polygon, one at each vertex, is 360

cpctc

corresponding parts in congruent triangles are congruent

isosceles triangle theorem

if two sides of a triangle are congruent, then the angles opposite those sides are congruent

HL

if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and leg of another right angle, then the triangles are congruent

midsegment

a segment connecting the midpoints of two sides

midsegment theorem

if a segment joins the midpoints of 2 sides of a triangle, then the segment is parallel to the third side and half its length

altitude

a perpendicular segment from a vertex to the line containing the side opposite that vertex

median

a segment that has a vertex of a triangle and the midpoint of the opposite side as its endpoints

concurrent

when 3 or more lines intersect in one point

circumcenter

point where the perpendicular bisectors intersect; perpendicular bisectors are concurrent at this point that is equidistant from the vertices

incenter

point where the angle bisectors intersect; angle bisectors are concurrent at this point that is equidistant from the sides

centroid

the point of concurrency of the medians of a triangle

centroid theorem

the length of the segment from the vertex to the centroid is twice the length of the segment from the centroid to the midpoint

negation

the opposite truth value of a statement

inverse

negates the hypothesis and conclusion of a conditional statement

contrapositive

switches the hypothesis and conclusion and negates them both

triangle inequality theorem

the sum of the lengths of any two sides of a triangle is greater than the third side

parallelogram

a quadrilateral with both pairs of opposite sides parallel

kite

a quadrilateral with two pairs of consecutive sides congruent and no opposite sides congruent

rhombus

a parallelogram with four congruent sides

rectangle

a parallelogram with four right angles

square

a parallelogram with four congruent sides and four right angles

trapezoid

a quadrilateral with exactly one pair of opposite sides parallel

isosceles trapezoid

a trapezoid whose nonparallel sides are congruent

parallelogram properties

opposite sides are congruent, opposite angles are congruent, diagonals bisect eachother, if three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal

rhombus properties

each diagonal of a rhombus bisects two angles of the rhombus; the diagonals of a rhombus are perpendicular

rectangle property

the diagonals of a rectangle are congruent