Term
|
Definition
| 1.The points on a line can be paired with the real numbers in such a way that any two points can have coordinates 0 and 1 |
|
|
Term
| Postulate 2 (Seg add post) |
|
Definition
| If point B is between A and C, the AB+BC=AC |
|
|
Term
| Postulate 3 (Protractor post) |
|
Definition
On line AB in any given plane, chose any point O between A and B. Consider that line OA and line OB and all the rays that can be drawn from O to one side of line AB. These rays can be paired with the real numbers from 0 to 180 in such a way that:
a. line OA is paired with 0, and line OB with 180
b. If line OP is paired with x, and line OQ with with y, then angle POQ= the absolute value of x-y. |
|
|
Term
| Postulate 4 (Angle Addition Post) |
|
Definition
| If point B lies in the exterior of angle AOC, then angle AOB + angle BOC = angle AOC |
|
|
Term
|
Definition
| A line contains at least two points; a plane contains at least three points not all in one line; space contains at least four points not all in one plane |
|
|
Term
|
Definition
| Through any two points there is exactly one line. |
|
|
Term
|
Definition
| Through any three points there is at least one plane, and through any three noncollinear points there is exactly one plane. |
|
|
Term
|
Definition
| If two points are in a plane , then the lines that contains those points is in that plane. |
|
|
Term
|
Definition
| If two planes intersect, then their intersection is a line. |
|
|
Term
|
Definition
| If two line intersect, then they intersect at exactly one point. |
|
|
Term
|
Definition
| Through a line and a pointnot in the line there is exactly one plane. |
|
|
Term
|
Definition
| If two lines intersect, then exactly one plane contains the lines. |
|
|
Term
| Therom 2-1 (midpoint theorem) |
|
Definition
| If M is the midpoint of line AB, then AM = 1/2AB and MB = 1/2AB |
|
|
Term
| Theorom 2-2 (angle bisector theorem) |
|
Definition
| If line BX is the bisector of angle ABC, then angle ABX = 1/2 angle ABC and angle XBC = 1/2 angle ABC |
|
|
Term
|
Definition
| Vertical angles are congruent |
|
|
Term
|
Definition
| If two lines are perpendicular, they form congruent, adjacent angles |
|
|
Term
|
Definition
| If two lines form congruent adjacent angles, then the lines are perpendicular |
|
|
Term
|
Definition
| If the exterior side of two adjacent acute angles are perpendicular, then the angles are complementary |
|
|
Term
|
Definition
| If two angles are supplements of congruent segments, then the wtwo angles are congruent. |
|
|
Term
|
Definition
| if two parallel planes are cut by a third plane, then the lines of intersection are parallel |
|
|
Term
|
Definition
| if two parallel lines are cut by a transversal, then corresponding angles are congruent |
|
|
Term
|
Definition
| if two parallel lines are cut by a transversal, then the alternate interior angles are congruent |
|
|
Term
|
Definition
| If two parallel lines are cut by a transversal, then the same side interior angles are supplementary |
|
|
Term
|
Definition
| if a transversal is perpendicular to on eof two parallel lines, then it is perpendicular to the onther one also. |
|
|
Term
|
Definition
| if two lines are cut by a transversal and corresponding angles are congruent, then then the lines are parallel |
|
|
Term
|
Definition
| if two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel |
|
|
Term
|
Definition
| If two lines are cut by a transversal and the same-side interior angles are supplementary, then the lines are parallel |
|
|
Term
|
Definition
| In a plane, two lines perpendicular to the same line are parallel |
|
|
Term
|
Definition
| Through a point outside a line, there is exactly one line parallel to the given line |
|
|
Term
|
Definition
| Through a point outside a line, there is exactly on eline perpendicular to the given line |
|
|
Term
|
Definition
| Two lines parallel to the third line are parallel to eachother |
|
|
Term
|
Definition
| The sum of the measures of the angles of a triangle is 180 |
|
|
Term
|
Definition
| If two angles of a triangle are congruent to two angles of another triangle, then the thrid angles are congruent. |
|
|
Term
|
Definition
| Each angle of an equiangular triangle has a measure of 60 |
|
|
Term
|
Definition
| In a triangle, there can be at most one right obruse angle. |
|
|
Term
|
Definition
| The accute angles of a right triangle are complementary |
|
|
Term
|
Definition
| The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles |
|
|
Term
|
Definition
| The sum of the measures of the angles of a convex polygonwith n sides is (n-2)180 |
|
|
Term
|
Definition
| The sum of th measures of the exterior angles of any convex polygon, one angle at each vertex, is 360 |
|
|
Term
|
Definition
| If three side of on etrianglr are congruent to three sides of another triangle, then the triangles are congruent |
|
|
Term
|
Definition
| If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. |
|
|
Term
|
Definition
| if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent |
|
|
Term
| Therom 4-1 (Isosceles Triangle Theorem) |
|
Definition
| If two sides of a triangle are congruent, then the angles oppisite those sides are congruent |
|
|
Term
|
Definition
| An equilateral triangle is also equiangular |
|
|
Term
|
Definition
| an equilateral triangle has 3 60 degree angles |
|
|
Term
|
Definition
| The bisector of the vertex angle of an isosceles is perpendicular to the base at its midpoint |
|
|
Term
|
Definition
| If two angles of a triangle are congruent, then the sides oppisite those angles are congruent. |
|
|
Term
|
Definition
| an equiangular triangle is also equilateral |
|
|
Term
|
Definition
| if two angles and a non-included side of on etriangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. |
|
|
Term
|
Definition
| If the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. |
|
|
Term
|
Definition
| If apoint lies on the bisecotr of a segment, then the point is equidistant from the endpoints of the segment. |
|
|
Term
|
Definition
| if a point is equidistant from the nedpoints of the segment, then the point lies on the perpendicular bisector of the segment |
|
|
Term
|
Definition
| If a point lies on the bisector of an angle, then the point is equidistant fom the sides of the angle |
|
|
Term
|
Definition
| if a point is equidistant from th e sides of an angle, then the point lies on the bisector of the angle. |
|
|
Term
|
Definition
| Oppisite sides of a prallelogram are congruent |
|
|
Term
|
Definition
| oppisite angles of a parallelogram are congruent |
|
|
Term
|
Definition
| Diagonals of a parallelogram bisect eachother |
|
|
Term
|
Definition
| If both pairs pf oppisite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram |
|
|
Term
|
Definition
| If one pair of oppisite sides of a quadrilateral are bothe congruent and parallel, then the quadrilateral is a parallelogram |
|
|
Term
|
Definition
| if both pairs of oppisite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram |
|
|
Term
|
Definition
| if the diagonals of a quadrilateral bisect eachother, then the quadrilateral is a parallelogram |
|
|
Term
|
Definition
| if two lines are parallel, then all points one one line are equidistant from the other line |
|
|
Term
|
Definition
| If three lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal. |
|
|
Term
|
Definition
| a line that contains the midpoint of one side of a triangle and is parallel to another side passes through the midpoint of the third side |
|
|
Term
|
Definition
the segment that joins the midpoints of two sides of a triangle
1)is parallel to the third side
2)is half as long as the third side |
|
|
Term
|
Definition
| the diagonals of a rectangle are congruent |
|
|
Term
|
Definition
| The diagonals of a rhombus are perpendicular |
|
|
Term
|
Definition
| Each diagonal of a rhombus bisects two angles of the rhombus |
|
|
Term
|
Definition
| the midpoint of the hypotenuse of a right triangle is equidistant from the three vertices |
|
|
Term
|
Definition
| If an angle of a parallelogram is a right agle, the the parallelogram is a rectangle |
|
|
Term
|
Definition
| if two consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus |
|
|
Term
|
Definition
| Base angles of an isosceles trapezoid are congruent |
|
|
Term
|
Definition
The median of a trapezoid
1) is parallel to the base
2) has a length equal to the average of the base lengths |
|
|
Term
|
Definition
| The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle. |
|
|
Term
|
Definition
| if one side of a triangle is longer than a second side, the the angle oppisite the first side is larger than the angle oppisite the second side. |
|
|
Term
|
Definition
| if one angle of a triangle is larger than a second angle, then the side oppisite the first angle is longer than the side oppisite the second angle |
|
|
Term
|
Definition
| The perpendicular segment from a point to a line is the shortest segment from the point to line |
|
|
Term
|
Definition
| The perpendicular segment from a point to a plane is the shortest segment from the point to the plane |
|
|
Term
|
Definition
| The sum of the lengths of any two sides of a triangle is greater than the length of the third side. |
|
|
Term
|
Definition
| if two sides of one triangle are congruent to two sides of another triangle, but the included angle of the first triangle si greater than the included angle of the second , then the third side of the first triangle os longer than the third side of the second triangle |
|
|
Term
|
Definition
| if two sides of one triangle are congruent to two side of another triangle, but the third side of the first triangle is longer than the third side of the second, then the included angle of the first triangle is larger than the included angle of the second. |
|
|
Term
|
Definition
| If two angles are complements of congruent angles (or of the same angle), then the two angles are congruent |
|
|
