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WilsonGeometry
Wilsons Definitions
| Question | Answer |
|---|---|
| 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 |
Created by:
arudow15
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