angle bisectors of a triangle

incenter

perpendicular bisectors of a triangle

circumcenter

medians of a triangle

2/3, centroid

altitudes

4/3, orthocenter

triangle inequality theorem

the sum of the lentghs of any 2 sides of a triangle is greater than the length of the third side

triangle side comparison theorem

if 2 angles of a triangle are not congruent, then the longer side lies opposite the larger angle

triangle angle comparison theorem

if 2 sides of a triangle are not congruent, then the larger angle lies opposite the longer side

hinge theorem

if 2 sides of 1 triangle are congruent to 2 sides of another triangle, but the included angle of the first triangle is larger than the included angle of the second trianlge, then the third side of the first triangle is greater than the third side of the second triangle

SAS postulate

if 2 sides and the included angle of 1 triangle are congruent to 2 sides and the included angle in a second triangle, then the 2 triangles are congruent.

third angle theorem

if 2 angles of 1 triangle are congruent to 2 angles in a second triangle, then their third angles are also congruent

HL theorem

if the hypotenuse and leg of 1 right triangle are congruent to the hypotenuse and leg of a second right triangle, then the 2 triangles are congruent

SSS postulate

if 3 sides of 1 triangle are congruent to 3 sides of a second triangle, then the 2 triangles are congruent.

CPCTC

Corresponding Parts of Congruent Triangles are Congruent

triangle exterior angle theorem

the exterior angle of a triangle is equal to the sum of its corresponding remote interior angles

isosceles triangle theorem

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

AAS theorem

if 2 angles and a non-included side of 1 triangle are congruent to 2 angles and a non-included side in a second triangle, then the 2 triangles are congruent

verticle angle theorem

verticle angles are congruent

theorem

in a coordinate plane, 2 nonvertical lines are perpendicular iff their slopes are negative reciprocals of each other

corresponding angles postulate

if a transversal intersects 2 parallel lines, then the corresponding angles are congruent

alternate interior angles theorem

if a transversal intersects 2 parallel lines, then the alternate interior angles are congruent

same side interior angles theorem

if a transversal intersects 2 parallel lines, then the same side interior angles are supplementary

midpoint theorem

if m is the midpoint of AB (line over), then AM=1/2 AB and BM=1/2 AB

Law of Detachment

if a conditional statement is true and its hypothesis is true, then its conclusion is true.

Law of Syllogism

2 conditionals lead to a third conditional

angle addition postulate

aap

converse

Q-->P

inverse

~P-->~Q

contrapositive

~Q-->~P

segment addition postulate

if a, b, and c are collinear points and b is betewwn a and c, then AB+BC=AC

supplementary angles

add up to 180

complemetary angles

add up to 90

3 undefined terms in geometry

plane, point, line

angle addition postulate

if point X lies in the interior of <ABC, then <ABX+<CBX=<ABC

angle bisector theorem

if BX (--> over) is the bisector of <ABC, then m<ABX=1/2 m<ABC and m<XBC=1/2 m<ABC

congruent supplements theorem

if 2 angles r supplementary to the same (or congruent angles), then the 2 angles are congruent.

congruent complements theorem.

if 2 angles r complementary to the same (or congruent angles), then the 2 angles are congruent.

linear pair postulate

linear pairs are supplementary

converse of the corresponding angles potulate

if the corresponding angles are congruent, then the transvesal intersects 2 parallel lines

converse of the alternate interior angles theorem

if the alternate interior angles are congruent, then the transvesal intersects 2 parallel lines

converse of the same side interior angles theorem

if 2 lines and a transveral form same side interior angles that are supplementary, then the 2 lines are parallel

converse of the alt. ext. angles theorem

if the alt. ext. angles are congruent, then the transvesal intersects 2 parallel lines

if 2 lines are parallel to the same line...

then they are parallel to each other

triangle angle sum theorem

the sum of the angle measures in a triangle is 180 degrees

interior angle sum of a polygon

(n-2)180 {n=# of sides}

ASA postulate

if 2 angles and the included side of 1 triangle are congruent to 2 angles and the included side of a second triangle, then the 2 triangles are congruent

HA theorem

right triangles only: hypotenuse-angle

LL theorem

right triangles only: leg-leg

LA theorem

right triangles only: leg-angle

converse of isosceles triangle theorem

congruent base angles = congruent sides

angle bisector theorem

if a point is on the angle bisector of an angle, then it is equidistant from the 2 sides of the triangle

permutation

pool P position

combination

pool C group

conditional statement

if-then P-->Q

biconditional

P<-->Q