# Essay, Research Paper: Theorems

## Mathematics

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Postulate1-3--given AB and a # r between 0 and 180, there is exactly one ray w/

endpoint A, extending on each side of AB, such that the measure of the angle

formed is r postulate1-4--if r is in the interior of pqs, then Mpqr+Mrqs=Mpqs.if

Mpqr+Mrqs then R is in thr interior of angle pqs postulate 2-2--through any 3

points not on the same line there is exactly one plane law of detachment--if

P--*Q is a true conditional and P is true, then Q is true law of syllogism--if

P--*Q and Q--*R are true conditionals, then P--*R is also true

theorem2-1--congruence of segments is reflexive, symmetric and transitive

theorem2-2--if 2 angles form a linear pair, then they r supplementary angles

theorem2-3--congruence of angles is reflexive, symmetric, and transitive

theorem2-4--angles supplementary to the same angle or to the congruent angles r

congruent theorem2-5--angles complementary to the same angle or to congruent

angles r congruent theorem2-6--all right angles r congruent theorem2-7--vertical

angles r congruent theorem2-8--perpindicular lines intersect to form 4 right

angles skew lines-2 lines r skew if they don’t intersect and r not in the same

plane postulate3-1-- if 2 // lines r cut by a transversal, then each pair of

corresponding angles is congruent theorem3-1--if 2 // lines r cut by a

transversal, then each pair of alternate interior angles in congruent

theorem3-2--if 2 // lines r cut by a transversal, then each pair of consec. int.

angles is supp. theorem3-3--if 2 // lines r cut by a transversal, then each pair

of alternate ext. angles is congruent theorem3-4--in a plane, if a line is perp.

to 1 of 2 // lines, then it is perp. to the other postulate3-4--2 nonvertical

lines have the same slope if and only if they r //. postulate3-5--2 nonvertical

lines r perp. if and only if the product of their slopes is -1 theorem4-3--the

measure of an exterior angle of a triangle is equal to the sum of the measures

of the 2 remote interior angles CPCTC- 2 triangles r congruent if and only if

their corresponding parts r congruent theorem4-4--congruence of triangles is

reflexive, transitive and symmetric theorem4-6--if 2 sides of a triangle r

congruent, then the angles opp. the sides r congruent theorem4-7--if 2 angles of

a triangle r congruent, then the sides opp. those angles r congruent

theorem4-3--a triangle is equilateral if and only if it is equiangular

theorem5-1 a point on the perp. bisector of a seg. is equidistant from the

endpoints of the seg. theorem5-2--a point equidistant from the endpoints of a

seg. lies in the perp. bisector of the seg. theorem5-3--a point on the bisector

of an angle is equidistant from the sides of the angle theorem5-4--a point in

the interior of or on an angle and equidistant from the sides of an angle lies

on the bisector of the angle theorem5-5--if the legs of 1 rt. triangle r

congruent to the corr. legs of another rt. triangle, then the triangles r

congruent theorem5-6--if the hypotenuse and an acute angle of 1 rt. triangle r

congruent to the hyp. and corr. acute angle of another rt. triangle, then the 2

triangles r congruent theorem5-9--if 1 side of a triangle is longer than the

other side,then the angle opp. the longer side is greater than the angle opp.

the shorter side theorem5-11--the perp.seg. froma point to a line is ythe

shortest seg. from the point to the line theorem5-12--the sum of the lenghts of

any 2 sides of a triangle is greater than the lenght of the third side

theorem6-1--opp. sides and angles of a parallelogram r congruent theorem6-4--the

diagonals of a parallelogram bisect each other theorem6-5--if both pairs of opp.

sides of a quad. r congruent, the the quad is a parallelogram theorem6-6--if 1

pair of opp. sides of a quad. r both parallel and congruent, then the quad. is a

parallelogram theorem6-7--if the diagonals of a quad. bisect each other, then

the quad. is a parallelogram theorem6-8--if both pairs of opp. angles in a quad

r congruent,then the quad is a parallelogram theorem6-9--if a paralellogram is a

rectangle then its diagonals r congruent theorem6-10--the diagonals of a rhombus

r perp. theorem6-11--each diagonal of a rhombus bisects a pair of opp. angles

theorem6-12--both pairs of base angles of an isoceles trapezoid r congruent

theorem6-13--the diagonals of an isoceles trapezoid r congrient theorem6-14--the

mediand of a trapezoid is parallel to the bases and its measure is one half the

sum of the measures of the bases.

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