# Wilsons Definitions

equidistant same distance from a single point
ruler postulate statement that is accepted as true without justification
congruent same size, same shape
postulate 5 the least number of points 2-line 3-plane (non collinear) 4-space(none coplanear)
postulate 6 2 points = exactly one line
postulate 7 3 points = one plane
postulate 8 two points on a plane means that line between is in the plane also
postulate 9 two planes intersect in a line
theorem 1-1 if two lines intersect then they intersect on one point
theorem 1-2 if i have a line and a point not on the line then there is exactly one plane
theorem 1-3 two lines intersect, one plane
perpendicular line theorem two lines and perpendicular if and onlt if they form two congruent and adjacent angles
complementary angle theorem if the exterior sides of two adjacent acute angles are perpendicular then the angles are compliments
SOSAC supplements of the same angle are congruent
COSAC compliments of the same angle are congruent
parallel coplanear lines that never intersect
skew lines noncoplanear lines that never intersect
proving lines are parallel corresponding angles are congruent
theorem 3-6 if same side interior angles are supplements then the lines are //
theorem 3-7 if two lines are perpendicular to the same line then the lines are //
theorem 3-5 if the alt int angles are congruent then the lines are //
theorem 3-8 given a point not on a line there exists exactly one // line through the point
theorem 3-10 if two lines are // to a third line then they are // to eachother
theorem 3-11 (triangle sum theorem) the sum of the angles is 180
corollary 1 triangle sum theorem
corollary 2 equiangular triangle the angles are 60
corollary 3 at most one right or obtuse angle
corollary 4 acute angles of a right triangle are compliments
SSS side, side, side
SAS side, angle, side
ASA angle, side, angle
AAS angle, angle, side
HL if the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle then the triangles are congruent
rectangle theorems a parallelogram with a right angle
rhombus theorems diagonals of a rhombus are perpendicular, diagonals of a rhombus bisect the angles of the rhombus, a parallelogram with two congruent consecutive sides is a rhombus
isosceles trapezoid congruent legs
median segment that joins the two midpoints of both legs
trapezoid theorem base angles are congruent
theorem 5-1 opposite sides of a parallelogram are congruent
theorem 5-2 opposite angles of a parallelogram are congruent
theorem 5-3 diagonals of a parallelogram bisect each other
theorem 5-4 if both pairs of opposite sides of a quadrilateral are both congruent then its a parallelogram
theorem 5-5 if one pair of opposite sides of a quadrilateral are both congruent and parallel then its a parallelogram
theorem 5-6 if both pairs of opposite angles of a quadrilateral are congruent then its a parallelogram
theorem 5-7 if the diagonals of a quadrilateral bisect each other then its a parallelogram
theorem 5-8 if two lines are parallel then all the points on one line are equidistant from the other line
theorem 5-9 if three parallel lines cut off congruent segments on one transversal then they cut off congruent segments on every transversal
theorem 5-10 a line that contains the midpoint of one side of a triangle and is parallel to another side passes through the midpoint on the third side
theorem 5-11 the segment that joins the midpoints of two sides of a triangle is parallel to the third side and is half the length of the third side
theorem 5-12 the diagonals of a rectangle are congruent
theorem 5-13 the diagonals of a rhombus are perpendicular
theorem 5-14 each diagonal of a rhombus bisects two angles
theorem 5-15 the midpoint of the hypotenuse of a right triangle is equidistant from the three vertices
theorem 5-16 if an angle of a parallelogam is a right angle then the parallelogram is a rectangle
theorem 5-17 if two consecutive sides of a parallelogram are congruent then the parallelogram is a rhombus
theorem 5-18 base angles of an isosceles trapezoid are congruent
theorem 5-19 the median of a trapezoid is parallel to the bases and has a length equal to the average of the base lengths