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Geometry Terms
Geometry terms
Term | Definition |
---|---|
Geometry | branch of mathematics that deals with points, lines, planes, and solids and examines their properties |
Point | Has no size, length, width, or height. It is represented by a dot and named by a capital letter. |
Line | Set of points that has infinite length and width but no height. We name this with a lower case letter or by any two points on the line. |
Plane | set of pints that has infinite length and width but no height. We name this with a capital letter. |
Space | Set of all point |
Collinear Points | points that lie on the same line |
noncollinear points | points that do not lie on the same line |
Coplanar Points | point that lie on the same plane |
Noncoplanar Points | points that do not lie on the same plane |
Segment | part of a line that consists of two points called endpoints and all points between them |
Ray | Is the part of a line that contains an endpoint and all points extending in the other direction |
congruent segments | segments that have the same length |
Bisectors of a segment | Line, ray segment, or plane that divides a segment into two congruent segments. |
Midpoint of a segment | a point that divides the segment into two congruent segments |
Acute angle | angle whose measure is between 0 and 90 degrees |
Right angle | angle whose measure is 90 degrees |
Obtuse angle | Angle whose measure is greater than 90 degrees but less than 180 degrees |
Straight angle | angle whose measure is 180 degrees |
Congruent angles | angles that have the same measure |
Angle bisector | ray that divides an angle into two congruent adjacent angles |
Triangle | The figure formed by three segments joining three noncollinear points. Each of the three points is a vertex of the triangle and the segments are sides. |
Acute triangle | triangle that has all acute angles |
Right triangle | Triangle with a right angle |
Obtuse triangle | Triangle with an obtuse angle |
Equilangular triangle | triangle with all angles congruent |
Scalene triangle | triangle with no sides congruent |
Isosceles triangle | Triangle with at least two sides congruent |
Equilateral triangle | Triangle with all sides congruent |
Adjacent angles | two coplanar angles with a common vertex and a common side between them |
Vertical angles | the non-adjacent angles formed by twointersecting lines |
Complementary angles | two angles whose sum is 90 degrees |
Supplementary angles | two angles whose sum is 180 degrees |
Perpendicular lines | two lines that intersect to form right angles |
Parallel lines | two line are parallel if they are coplanar and do not intersect |
Skew lines | Are noncoplanar lines they will not intersect |
Polygon | Union of three or more coplanar segments that meet only at endpoints such that at most two segments meet at one endpoint and each segment meets exactly two other segments |
Regular polygon | polygon which is equilateral and equiangular |
Congruent Triangles | a triangle that has corresponding sides and corresponding angles congruent |
Median of a triangle | segment from the vertex of the triangle to the midpoint of the other side |
Altitude of a triangle | segment from the vertex of a triangle perpendicular to the line containing the opposite side |
Parallelogram | quadrilateral with both pairs of opposite sides parallel |
Rectangle | Parallelogram with a right angle |
Rhombus | Parallelogram with consecutive sides congruent |
Square | all sides congruent and all four right angles |
Trapezoid | quadrilateral with exactly one pair of opposite sides parallel |
Ratio | comparison of two numbers by division |
Proportion | equation that states that two ratios are equal |
Pythagorean Theorem | in a right triangle, the sum of the squares of the legs is equal to the square of the hypotenuse |
Circle | the set of points in a plane that are equidistant from a fixed point called the center |
Radius | Segment whose endpoints are the center of the circle and a point on the circle |
Chord | segment that connects two points on the circle |
Diameter | chord that passes through the center of the circle |
Secant | line that intersects a circle in two points |
Tangent | line in the plane of the circle the intersects the circle in one point |
Concentric Circles | two or more circles in the same plane with the same center |
Congruent Circles | circles that have congruent radii |
Sphere | set of points in space a given distance from a given point called the center |
Arc | consists of two points and the continuous part of a circle between them |
Semi-Circle | arc whose endpoints are the endpoints of a diameter |
Minor arc | arc whose measure is less than a semi-circle or 180 degrees |
major arc | arc whose measure is greater than a semi-circle of 180 degrees |
central angle of a circle | angle whose vertex is the center of the circle and whose rays are radii of the circle |
Congruent arcs | arcs with equal measure in the same circle or in congruent circles |
Inscribed angles | angle whose vertex is on the circle and whose sides are chords of the circle |
bases | congruent polygons lying in parallel planes |
Altitude | segment joining the two base planes and perpendicular to both |
Lateral faces | faces of a prism that are not its bases |
Lateral edges | intersection of adjacent lateral faces |
Lateral area | Sum of the area of its lateral faces |
Surface area | sum of the area of all faces |
Volume | number of cubic units contained in a solid |
Right prism | a prism whose lateral faces are rectangles |
oblique prism | a prism whose lateral faces are parallelograms |
cube | a prism where all sides are squares |
Triangular prism | a prism whose parallel faces are congruent triangles |
Cylinder | has two congruent circular bases in parallel planes |
Cone | has a vertex and a circular base |
Line of symmetry | divides a figure into two congruent halves that reflect each other |
Perimeter | the distance around the polygon |
Area | the number of square units needed to cover the figure |
Circumference | the distance around a circle |
conditional statement | a statement that can be written in if-then form |
Hypothesis | in a conditional statement, it is the statement that immediately follows the word if |
Conclusion | in a conditional statement, it is the statement that immediately follows the word then |
Converse | The statement formed by exchanging the hypothesis and the conclusion of a conditional statement |
Inverse | the statement formed by negating both the hypothesis and the conclusion of a conditional statement |
Contrapositive | the statement formed by negating both the hypothesis and conclusion of the converse of a conditional statement |
Biconditional | the conjunction of a conditional statement and its converse |
Proof | a logical argument in which each statement you make is supported by a statement that is accepted as true |
Postulate | a statement that describes a fundamental relationship between basic terms of geometry. These are accepted as true without proof. |
Theorem | A statement or conjecture that can be proven true by given, definitions, postulates, or already proven theorems. |
Two column proof | a formal proof that contains statements and reasons organized in two columns |
Paragraph proof | an informal proof written in the form of a paragraph that explains why a conjecture for a given situation is true |
Flow proof | a proof that organizes statements in logical order, starting with given statements |
Sine | for an acute angle of a right triangle, the ratio of the measure of the leg opposite the acute angle to the measure of the hypotenuse |
Cosine | for an acute angle of a right triangle, the ratio of the measure of the leg adjacent to the acute angle to the measure of the hypotenuse |
Tangent | for an acute angle of a right triangle, the ratio of the measure of the leg opposite the acute angle to the measure of the leg adjacent to the acute angle |