# Theorems

Updated April 14, 2020
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Theorems postulate1-3–given AB and a # r between 0 and 180, there is exactly one ray w/ endpoint A,extending on each side ofAB, 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 dont intersect and r not in the samn 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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