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Geo Exam-Fall

Geo Exam-Fall
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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