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Geometry Ch. 1
Foundations for Geometry- vocabulary
| Term | Definition |
|---|---|
| undefined term | a basic figure that is not defined in terms of other figures: point, line, plane |
| point | (an undefined term in geometry) it names a location and has no size |
| line | (an undefined term in geometry) a straight path that has no thickness and extends forever |
| plane | (an undefined term in geometry) a flat surface that has no thickness and extends forever |
| collinear | points that lie on the same line |
| coplanar | points that lie on the same plane |
| segment of a line | a part of a line consisting of two endpoints and all points between them |
| endpoint | a point at an end of a segment of the starting point of a ray |
| ray | a part of a line that starts at an endpoint and extends forever in one direction |
| opposite rays | two rays that have a common endpoint and form a line |
| postulate (also called an axiom) | a statement that is accepted as true without proof |
| Postulate 1-1-1 | Through any two points there is exactly one line. |
| Postulate 1-1-2 | Through any three noncollinear points there is exactly one plane containing them. |
| Postulate 1-1-3 | If two points lie in a plane, then the line containing those points lies in the plane. |
| Postulate 1-1-4 | If two lines intersect, then they intersect in exactly one point. |
| Postulate 1-1-5 | If two planes intersect, then they intersect in exactly one line. |
| coordinate | a number used to identify the location of a point |
| distance between two points | the absolute value of the difference of the coordinates of the points |
| length | the distance between the two endpoints of a segment |
| congruent segments | two segments that have the same length |
| construction | a method of creating a figure that is considered to be mathematically precise; uses a compass and straightedge, geometry software, or paper folding |
| between | Given three points A, B, and C, B is between A and C if and only if all three of the points lie on the same line, and AB + BC = AC. |
| midpoint | the point that divides a segment into two congruent segments |
| bisect | to divide into two congruent parts |
| segment bisector | a line, ray, or segment that divides a segment into two congruent segments |
| Ruler Postulate (1-2-1) | The points on a line can be put into a one-to-one correspondence with the real numbers. |
| Segment Addition Postulate (1-2-2) | If B is between A and C, then AB + BC = AC. |
| angle | a figure formed by two rays with a common endpoint |
| vertex of an angle | the common endpoint of the sides of the angle |
| interior of an angle | the set of all points between the sides of an angle |
| exterior of an angle | the set of all points outside an angle |
| degree | a unit of angle measure (1/360 of a circle) |
| acute angle | an angle that measures greater than 0º and less than 90º |
| right angle | an angle that measures 90º |
| obtuse angle | an angle that measures greater than 90º and less than 180º |
| straight angle | a 180º angle |
| congruent angles | angles that have the same measure |
| angle bisector | a ray that divides an angle into two congruent angles |
| Protractor Postulate (1-3-1) | Given line AB and a point O on line AB, all rays that can be drawn from O can be put into a one-to-one correspondence with the real numbers from 0 to 180. |
| Angle Addition Postulate (1-3-2) (∠ Add. Post.) | If S is the in the interior of ∠PQR, then m∠PQS + m∠SQR = m∠PQR. |
| adjacent angles | two angles in the same plane with a common vertex and a common side but no common interior points |
| linear pair | a pair of adjacent angles whose noncommon sides are opposite rays (form a straight line) |
| complementary angles | two angle whose measures have a sum of 90º |
| supplementary angles | two angles whose measures have a sum of 180º |
| vertical angles | the nonadjacent angles formed by two intersecting lines |
| perimeter (definition) | the sum of the sides lengths of a close plane figure |
| area (definition) | the number of nonoverlapping unit squares of a given size that will exactly cover the interior of a plane figure |
| base of a triangle | any side of a triangle |
| height of a triangle | a segment from a vertex that forms a right angle with a line containing the base |
| diameter | a segment that has endpoints on the circle and that passes through the center of the circle |
| radius of a circle | a segment who endpoints are the center of a circle and a point on the circle |
| circumference (definition) | the distance around the circle |
| pi (π) | the ratio of the circumference of a circle to its diameter, ≈ 3.14... |
| coordinate plane | a plane that is divided into four regions by a horizontal line called the x-axis and a vertical line called the y-axis |
| leg of a right triangle | one of the two sides of the right triangle that form the right angle |
| hypotenuse | the side opposite the right angle in a right triangle |
| Pythagorean Theorem (Thm 1-6-1) | In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. (a^2 + b^2 = c^2) |
| transformation | a change in the position, size, or shape of a figure or graph |
| preimage | the original figure in a transformation |
| image | a shape that results from a transformation of a figure known as the preimage |
| reflection | a transformation across a line such that the line of reflection is the perpendicular bisector of each segment joining each point and its image |
| rotation | a transformation about the point P such that each point and its image are the same distance from P |
| translation | a transformation that shifts or slides every point of a figure or graph the same distance in the same direction |
| congruent | having the same size and shape, denoted by ≅ |
| Pythagorean Triples | a set of three nonzero whole numbers that satisfy the Pythagorean Theorem (such as {3,4,5}, {5,12,13}, or {7,24,25}) |
Created by:
rismith
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