| Term | Definition |
|---|
| Point | An infinitely small location in space |
| Space | The set of all points in 3 dimensions |
| Plane | A set of all points in 2 dimensions |
| Line | An infinite set of contiguous points on a plane that extend indefinitely in opposite directions such that the ratio of the vertical and horizontal displacements between any two points in the set is constant |
| Ray | A part of a line that extends indefinitely in one direction from a terminal point |
| Line segment | A part of a line that extends between two terminal points |
| The Ruler Postulate | The points on any line can be paired with real numbers such that given points P and Q on a line, P corresponds to 0 and Q corresponds to a positive number |
| The Segment Addition Postulate | If Q is between P and R then PQ+QR=PR and if PQ+QR=PR then Q is between P and R |
| Angle | A two-dimensional figure formed by two rays with a common terminal point called a vertex |
| The Protractor Postulate | Given ray AB and a number R between 0 and 180 there is exactly one ray with endpoint A extending on either side of ray AB such that the measure of the angle formed is R |
| The Angle Addition Postulate | If R is in the interior of angle PQS then the mAnglePQR+mAngleRQS=mAnglePQS and if mAnglePQR+mAngleRQS=mAnglePQS then R is in the interior of Angle PQS |
| Adjacent Angles | Two angles that share a common plane, a common side, and a common vertex, but do not share any common interior points |
| Supplementary Angles | Two angles whose measures sum to 180 |
| Complementary Angles | Two angles whose measures sum to 90 |
| Acute Angle | An angle whose measure is between 0 and 90 |
| Right Angle | An angle whose measure is equal to 90 |
| Obtuse Angle | An angle whose measure is greater than 90 but less than 180 |
| Straight Angle | An angle whose sides form opposite rays, An angle whose measure is 180 |
| Linear Pair | Two angles whose non-common sides form opposite rays |
| Supplement Theorem | If two angles form a linear pair then they are supplementary |
| Angle bisector | A line, ray, or plane that divides an angle into two congruent angles |
| Vertical Angles | Two non-adjacent angles formed by intersecting lines |
| Perpendicular lines | Two lines that intersect to form a right angle |
| Congruent Angles | Angles that have the same size and shape |
| Midpoint | The midpoint M of line segment PQ is the point between P and Q such that PM=MQ |
| The Midpoint Theorem | If M is the midpoint of line segment AB then line segment AM is congruent to line segment MB |
| Reflexive Property of Congruent Segments | If there is a segment, it is reflexive |
| Properties of Congruent Angles | Congruence of angles is reflexive, symmetric, and transitive |
| Skew lines | Two lines that do not intersect that are not on the same plane |
| Parallel Lines | Two lines on the same plane that at every point are equal distance apart |
| Corresponding Angles Postulate | If two parallel lines are cut by a transversal then each pair of correspoinding angles is congruent |
| Alternate Interior Angles Theorem | If two parallel lines are cut by a transversal then each pair of alternate interior angles is congruent |
| Consecutive Interior Angles Theorem | If two parallel lines are cut by a transversal then each pair of consecutive interior angles is supplementary |
| Alternate Exterior Angles Theorem | If two parallel lines are cut by a transversal then each pair of alternate exterior angles is congruent |
| Perpendicular Transversal Theorem | In a plane, if a line is perpendicular to one of two parallel lines, it is perpendicular to the other |
| Slope | The slope m of a line containing two points with coordinates (x1, y1) and (x2, y2) is given by the formula m=(y2-y1)/(x2-x1), where x1 does not equal x2 |
| Lynchpin Postulate | If 2 lines in a plane are cut by a transversal so that corresponding angles are congruent, then the lines are parallel |
| Parallel Postulate | If there is a line and a point not on the line then there exists exactly 1 line through the point that is parallel to the given line |
| Distance From a Line To a Point Not On the Line | The length of the segment perpendicular to the line from the point |
| Distance Between 2 Parallel Lines | The distance between 1 of the lines and any point on the other line |
| Angle Sum Theorem | The angles in a triangle sum to 180 |
| Third Angle Theorem | If 2 angles of 1 triangle are congruent to 2 angles of a second triangle then the third angles of the triangles are congruent |
| Exterior Angle Theorem | The measure of an exterior angle of a triangle is = to the sum of the measures of the two remote interior angles |
| SSS Postulate | If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent |
| SAS Postulate | 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. |
| ASA Postulate | If two angles and the included side of one triangle are congruent to the corresponding angles and side of another triangle, the triangles are congruent. |
| AAS | If two angles and a non-included side of one triangle are congruent to the corresponding two angles and side of a second triangle, the two triangles are congruent. |
| Isosceles Triangle Theorem | If two sides of a triangle are congruent, then the angles opposite those sides are congruent |
| Not Isosceles Triangle Theorem | If two angles of a triangle are congruent, then the sides opposite those angles are congruent |
| Median | A special line segment in a triangle that extends from a vertex to the midpoint of the opposite side |
| Any point on the perpendicular bisector | Of a segment is equidistant from the endpoints of the segment |
| Any point equidistant from the endpoints | Of a segment lies on the perpendicular bisector of the segment |
| Any point on the bisector of | An angle is equidistant from the sides of the angle |
| Any point on or in the interior of an | Angle and equidistant from the sides of an angle lies on the bisector of the angle |
| Angle bisector of a triangle | A segment that bisects an angle of the triangle and has one endpoint at a vertex of the triangle and the other endpoint at another point on the triangle. |
| Perpendicular bisector of a triangle | A line or line segment that passes through the midpoint of a side of a triangle and is perpendicular to that side |
| Altitude of a triangle | A segment from a vertex of a triangle to the line containing the opposite side and perpendicular to the line containing that side |
| LL | If the legs of 1 right triangle are cognruent to the corresponding legs of another right triangle, then the triangles are congruent |
| HA | If the hypotenuse and an acute angle of 1 right triangle are congruent to the hypotenuse and an acute angle of another right triangle then the 2 triangles are congruent |
| LA | If one leg and an acute angle of 1 right triangle are congruent to the corresponding leg and acute angle of another right triangle, then the triangles are congruent |
| HL | If the hypotenuse and a leg of 1 right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent |
| Pi r2 | Area circle |
| Pi D | circumference |
| 1/2 bh | triangle |
| bh | square |
| split it up and add it up | area irregular figure |
| what are the terms point, line, and plane referred as? | Undefined |
| what are points in generals | locations |
| points are named using what? | capital letter |
| a line is what | stream points |
| points that lie of the same line are called what? | collinear |
| points that don't lie of the same line are called what? | noncollinear |
| what is a postulate? | a statement that is accepted as true without proof |
| what is a theorem? | a statement that has been proven |
| what is a plane? | a flat surface that extends indefinitely in all directions |
| coplaners are what? | points that lie in the same plane |
| what is a noncoplanar? | Points that do not line in the same plane |
| In geometry, the set of all points is called what? | space |
| what is zero dimensional? | a point |
| What are the 5 ways to prove triangles congruent? | SSS, SAS, AAS, ASA, HL |
| What is a conditional statement? | p-->q |
| What is a converse? | q-->p |
| What is a inverse? | ~p-->~q |
| What is a contrapositive? | ~q-->~p |
| What is a biconditional statement? | p<-->q |
| How many lines exist between two pts. | one line |
| What are collinear pts? | pts. on the same line |
| What are coplaner pts? | pts. on the same plane |
| What is a linear pair? | angles adding up to 180 |
| Where do the Perpendicular Bisectors meet? | Circumcenter |
| Where do the Angle Bisectors meet? | Incenter |
| Where do the medians meet? | centroid |
| Where do the altitudes meet? | orthocenter |
| acute angle | an angle with a measure greter than 0 and less that 90degrees |
| right angle | An angle that measures 90 degrees |
| abtuse angle | An angle that is greater than 90 and less than 180 degrees |
| straight angle | An angle that measures 180 degrees |
| compelmentary | Two angles are complementary if the sum of their measures is 90 degrees |
| supplementary | Two angles are supplenebtar uf gte syn if gteur measures is 180 degrees |
| adjacent | two or more angles intersects |
| vertical | Congruent angles formed by the interscting of two lines. |
| conjecture | an unproven statement that is passed on observations |
| inductive reasoning | process that includes looking for patterns and making conjectures |
| counter example | an example that shows a conjecture is false |
| definition | uses known words to describe a new word |
| undefined terms | a word, such as point, line, or phrase that is not formally defined, although there is general agreement about what the word means |
| point | a point has no dimension |
| line | a line extends in one dimension |
| plane | a plane extends in 2 dimensions |
| collinear points | points that lie on the same line |
| coplanar points | points that lie on the same plane |
| line segment | parts of a line that consists of 2 points, called endpoints, and all points on the line that are btwn the endpoint |
| ray | part of a line that consists of a point, called an initial point, and all points on the line that extend in one direction |
| opposite rays | if C is between A and B, the CA and CB are opposite rays |
| intersect | to have one or more points in common |
| intersection | the set of points that two or more geometric figures have in common |
| postulates | rules that are accepted without proof |
| coordinate | the real number that corresponds to a point on a line |
| distance | the distance between 2 points |
| distance formula | - |
| angle | consists of two different rays that have the same initail point |
| side | rays are the sides of the angle |
| vertex | the initial point of an angle |
| congruent angles | angles that have the same measure |
| interior of an angle | all points btwn the points that lie on each sides of the angles |
| exterior of an angle | all points not on the angle or in its interior |
| acute angle | an angle with measure btwn 0* and 90* |
| right angle | an angle with measure equal to 90* |
| obtuse angle | an angle with measure btwn 90* and 180* |
| straight angle | an angle with measure equal to 180* |
| adjacent angles | two angles with a common vertex and side but no common interior points |
| midpoint | the point that divides or bisects a segment into two congruent segments |
| bisect | to divide into two congruent parts |
| segment bisector | a segment, ray, line, or plane that intersects a segment at its midpoint. |
| midpoint formula | - |
| angle bisector | a ray that divides an angle into two adjacent angles that are congruent |
| vertical angles | two angles whose sides form two pairs of opposite rays |
| linear pair | two adjacent angles whose noncommonsides are opposite rays |
| complementary angles | two angles whose measures have the sum of 90* |
| supplementary angles | two angles whose measures have the sun 180* |
| parallel lines | two lines that are coplanar and do not intersect |
| skew lines | two lines that do not intersect and are not coplanar |
| parallel planes | two planes that do not intersect |
| transversal | a line that intersects two or more coplanar lines at different points |
| corresponding angles | two angles that are formed by two lines and a transversal and occupy corresponding positions |
| alternate exterior angles | 2 angles that are formed by 2 lines and a transversal and that lie outside the 2 lines on opposite sides of the transversal |
| alternate interior angles | 2 angles that are formed by 2 lines and a transversal and that lie between the 2 lines on opposite sides of the transversal |
| consecutive interior angles | 2 angles that are formed by 2 lines and a transversal and that lie between the 2 lines on the same side of the transversal |
| triangle | a figure formed by 3 segments joining 3 non collinear points called vertices |
| equilateral triangle | a triangle with 3 congruent sides |
| isosceles triangle | a triangle with at least 2 congruent sides |
| acute triangle | a triangle with 3 acute angles |
| equiangular triangle | a triangle with 3 congruent angles. |
| scalene triangle | a triangle with no congruent sides |
| right triangle | a triangle with 1 right angle |
| obtuse triangle | a triangle with 1 obtuse angle |
| vertex of a triangle | each of the 3 points joining the sides of a triangle |
| adjacent sides | 2 sides of a triangle with a common vertex |
| hypotenuse | in aright triangle the side opposite the right angle |
| interior angles | the 3 original angles of a triangle |
| exterior angles | angles that are adjacent to the interior angles |
| area | the number of square units needed to cover the surface of a figure |
| length | a unit used to measure how long something is |
| perimeter | the distance around an object |
| unit of measurement | a precisely fixed quantity used for measuring |
| width | a unit of measure for how wide something is |
| rectangle | a figure with four sides and four right angles |
| square | a polygon with four equal sides and four right angles |
| angle | the amount of turning or opening between two rays that have the same endpoint |
| acute angle | an angle that measures less than 90` |
| obtuse angle | an angle that measures more than 90` |
| right angle | an angle that measures exactly 90` |
| degree | unit of measure for angles |
| vertex | the point at which two sides of an angle meet |
| triangle | a three sided figure |
| equilateral triangle | a three sided figures which all sides and angles are equal |
| quadrilateral | a polygon with four sides and four angles |
| rhombus | a parellelogram whose four sides are congruent and whose opposite angles are congruent |
| hexagon | a six sided figure with six sides and angles |
| trapezoid | a quadrilateral with only one pair of parallel sides |
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