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Final Exam G-Fall-17
Term | Definition |
---|---|
Complementary angles | Two positive angles whose measures have the sum of 90° |
Midpoint | Point that divides the segment into two congruent segments |
Point | Has no dimension |
Obtuse | An angle that measures greater than 90° and less than 180° |
Collinear | Points that lie on the same line |
Plane | Has two dimensions |
Segment bisector | A point, ray, line segment, or plane that intersects the segment at its midpoint |
Congruent | Segments or angles that have the same measure |
Adjacent angles | Two angles that share a common vertex and side, but have no common interior points |
Line | Has one dimension |
Inductive reasoning | A process that includes looking for patterns and making conjectures. |
A biconditional statement | A statement that contains the phrase “if and only if”. |
If-then form | A conditional statement in the form “if p, then q” |
Conclusion | The “then” part of a conditional statement written in if-then form. |
Inverse | The statement formed by negating both the hypothesis and conclusion of a conditional statement |
Conditional statement | A logical statement that has a hypothesis and a conclusion. |
converse | The statement formed by exchanging the hypothesis and conclusion of a conditional statement |
Hypothesis | The “if” part of a conditional statement written in if-then form. |
Deductive reasoning | A process that uses, facts, definitions, accepted properties, and the laws of logic to form a logical argument. |
Contrapositive | The statement formed by negating both the hypothesis and conclusion of the converse of a conditional statement. |
Transversal | A line intersects two or more coplanar lines at different points. |
Alternate interior angles | Two angles, which are formed by two lines and a transversal, that lie between the two lines and on opposite side of the transversal. |
Corresponding angles | Two angles, which are formed by two lines and a transversal, that are in corresponding positions. |
Consecutive angles | Two angles, which are formed by two lines and a transversal, that lie between the two lines and on same side of the transversal. |
Alternate exterior angles | Two angles, which are formed by two lines and a transversal, that lie outside the two lines and on opposite side of the transversal. |
Parallel lines | Coplanar lines that do not intersect |
Vertical angles | Two angles whose sides from two pairs of opposite rays |
Perpendicular lines | Two lines that intersect to form right angles |
Linear pair | Two adjacent angles whose noncommon sides are opposite rays |
Skew | Lines that do not intersect and are not coplanar |
Reflection | A transformation that uses a line like a mirror to reflect a figure. |
Similar figures | Geometric figures that have the same shape but not necessarily the same size. |
Vector | A quantity that has both direction and magnitude and is represented in the coordinate plane by an arrow drawn from one point to another. |
Dilation | A transformation in which a figure is enlarged or reduced with respect to a fixed point. |
Transformation | A function that moves or changes a figure in some way to produce a new figure. |
Translation | A transformation that moves every point of a figure the same distance in the same direction. |
Rigid motion | A transformation that preserves length and angle measure. |
Rotation | A transformation in which a figure is turned about a fixed point. |
Scale factor | The ratio of the lengths of the corresponding sides of the image and the preimage of a dilation |
Congruent figures | Geometric figures that have the same size and shape |
Exterior angles | The side opposite the right angle of a right triangle |
Interior angles | Angles of a polygon |
Base of an isosceles triangle | The side of an isosceles triangle that is not one of the legs |
Vertex angle | The angle formed by the legs of an isosceles triangle |
Corresponding parts | A pair of sides or angles that have the same relative position in two congruent figures |
Legs of an right triangle | The sides adjacent to the right angle of a right triangle |
Exterior angles | Angles that form linear pairs with the interior angles of a polygon |
Base angles of an isosceles triangle | The two angles adjacent to the base of an isosceles triangle |
Coordinate proof | A style of proof that involves placing geometric figures in a coordinate plane |
Legs of an isosceles triangle | The two congruent sides of an isosceles triangle |
Median | A segment from a vertex of a triangle to the midpoint of the opposite side. |
Equidistant | A point that is equal distance from two figures |
Orthocenter | The point of concurrency of the lines containing the altitudes of the triangle. |
Incenter | The point of concurrency of the angle bisectors of a triangle. |
Altitude | The perpendicular segment from a vertex of a triangle to the opposite side or to the line that contains the opposite side |
Centroid | The point of concurrency of the three medians of a triangle. |
Point of concurrency | The point of intersection of concurrent lines, rays, or segments |
Midsegment | A segment that connects the midpoints of two sides of a triangle |
Concurrent | Three or more lines, rays, or segments that intersect in the same point |
Circumcenter | The point of concurrency of three perpendicular bisectors of a triangle |
Isosceles Trapezoid | A trapezoid with congruent legs. |
Rectangle | A parallelogram with four right angles. |
Trapezoid | A quadrilateral with exactly one pair of parallel sides |
Diagonals | A segment that joins two nonconsecutive vertices of a polygon. |
Parallelogram | A quadrilateral with both pairs of opposite sides parallel |
Rhombus | A parallelogram with four congruent sides |
Regular polygon | A convex polygon that is both equilateral and equiangular |
Equiangular polygon | A polygon in which all angles are congruent |
Square | A parallelogram with four congruent sides and four right angles. |
Kite | A quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent. |
Inverse tangent | An inverse trigonometric ratio, abbreviated . |
Inverse cosine | An inverse trigonometric ratio, abbreviated . |
Inverse sine | An inverse trigonometric ratio, abbreviated |
Angle of elevation | The angle that and upward line of sight makes with a horizontal line. |
Angle of depression | The angle that a downward line of sight makes with a horizontal line. |
Trigonometric ratio | A ratio of the lengths of two sides in a right triangle |
Pythagorean triple | A set of three positive integers, a, b, and c that satisfy the equation . |
Sine | A trigonometric ratio for acute angles that involves the lengths of the opposite leg and the hypotenuse of a right triangle. |
Tangent | A trigonometric ratio for acute angles that involves the lengths of a right triangle |
Cosine | A trigonometric ratio for acute angles that involves the lengths of the adjacent leg and the hypotenuse of a right triangle |
Standard equation of a circle | , where r is the radius and is the center. |
Minor arc | An arc with a measure less than 180°. |
Major arc | An arc with a measure greater than 180°. |
Semicircle | An arc with endpoints that are the endpoints of a diameter and measures exactly 180°. |
Central angle | An angle whose vertex is the center of a circle |
Circle | The set of all points in a plane that are equidistant from a given point |
Center | The point from which all points on a circle are equidistant. |
Radius | A segment whose endpoints are the center and any point on a circle. |
Chord | A segment whose endpoints are on a circle. |
Diameter | A chord that contains the center of a circle. |
Volume | The number of cubic units contained in the interior of a solid |
Sector of a circle | The region bounded by two radii of the circle and their intercepted arc |
Chord of a sphere | A segment whose endpoints are on a sphere |
Arc length | A portion of the circumference of a circle |
Face | A flat surface of a polyhedron |
Polyhedron | A solid that is bounded by polygons |
Edge | A line segment formed by the intersection of two faces of a polyhedron |
Apothem of a regular polygon | The distance from the center to any side of a regular polygon |
Circumference | The distance around a circle |
Density | The amount of matter that an object has in a given unit of volume |