Geometry Definitions Flashcards
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Questions and Answers

What is the definition of 'point'?

  • A location (correct)
  • A type of angle
  • Lines in the same plane
  • A solid figure

What is the circumference?

The distance around a circle

What does coplanar mean?

Points that lie on the same plane

What is perimeter?

<p>The sum of the lengths of the sides of a polygon</p> Signup and view all the answers

What are undefined terms in geometry?

<p>Points, planes, lines in geometry</p> Signup and view all the answers

What is an acute angle?

<p>An angle with a measure greater than 0° and less than 90°</p> Signup and view all the answers

What are adjacent angles?

<p>Angles that have the same vertex, share a common side, and do not overlap</p> Signup and view all the answers

What is an angle?

<p>A figure formed by two rays with a common endpoint</p> Signup and view all the answers

What is an angle bisector?

<p>A ray whose endpoint is the vertex of the angle and is located in the interior of the angle</p> Signup and view all the answers

What is area in geometry?

<p>The number of square units needed to cover a surface enclosed by a geometric figure</p> Signup and view all the answers

What is a base in geometry?

<p>The faces on the top and bottom of the figure</p> Signup and view all the answers

What does it mean for a point to be 'between' in geometry?

<p>Point R is between points P and Q if and only if R, P, and Q are collinear and PR + RQ = PQ</p> Signup and view all the answers

What does collinear mean?

<p>Three or more points that lie on the same line</p> Signup and view all the answers

What are complementary angles?

<p>Two angles are complementary if the sum of their measures is 90°</p> Signup and view all the answers

What does concave mean in terms of polygons?

<p>A polygon for which a point on at least one of its diagonals lies outside the polygon</p> Signup and view all the answers

What is a cone in geometry?

<p>A three-dimensional figure with one circular base and one vertex</p> Signup and view all the answers

What does congruent mean?

<p>Having the same measure</p> Signup and view all the answers

What is construction in geometry?

<p>The process of drawing a figure using only a compass and a straightedge</p> Signup and view all the answers

What does convex mean?

<p>A polygon for which all diagonals are located in the interior of the polygon</p> Signup and view all the answers

What is a cylinder?

<p>A solid figure whose bases are formed by congruent circles in parallel planes</p> Signup and view all the answers

What is a degree?

<p>The most common unit of measure for angles</p> Signup and view all the answers

What does distance refer to in geometry?

<p>The distance between two points</p> Signup and view all the answers

What is an edge in geometry?

<p>The intersection of faces of a three-dimensional figure</p> Signup and view all the answers

What is an equilateral polygon?

<p>A triangle having all three sides congruent and all three angles congruent</p> Signup and view all the answers

What is an equiangular polygon?

<p>A triangle with three congruent angles</p> Signup and view all the answers

What does exterior mean in terms of angles?

<p>All points outside the sides of the angle</p> Signup and view all the answers

What is the face of a figure?

<p>Surface of a figure</p> Signup and view all the answers

What does interior mean in terms of angles?

<p>All points between the two sides of an angle</p> Signup and view all the answers

What is the intersection in geometry?

<p>The set of elements common to two or more sets</p> Signup and view all the answers

What is a line in geometry?

<p>A never-ending straight path</p> Signup and view all the answers

What is a linear pair?

<p>Points upon a line</p> Signup and view all the answers

What is a line segment?

<p>Part of a line containing two endpoints and all the points between them</p> Signup and view all the answers

What is a midpoint?

<p>On a line segment, the point that is halfway between the endpoints</p> Signup and view all the answers

What is an n-gon?

<p>A polygon with n sides</p> Signup and view all the answers

What is an obtuse angle?

<p>An angle that measures more than 90° but less than 180°</p> Signup and view all the answers

What are opposite rays?

<p>Two rays that are part of the same line and have only their endpoints in common</p> Signup and view all the answers

What does perpendicular mean?

<p>Lines which meet to form right angles and whose slopes have a product of -1</p> Signup and view all the answers

What is a plane in geometry?

<p>A two-dimensional flat surface that extends in all directions</p> Signup and view all the answers

What is a polygon?

<p>A simple closed figure in a plane formed by three or more line segments</p> Signup and view all the answers

What is a polyhedron?

<p>A solid with four or more flat surfaces that are polygonal regions</p> Signup and view all the answers

What is a prism?

<p>A polyhedron with two parallel, congruent faces called bases</p> Signup and view all the answers

What is a pyramid?

<p>A solid figure that has a polygon for a base and triangles for sides</p> Signup and view all the answers

What is a ray?

<p>A part of a line that extends indefinitely in one direction from a fixed point</p> Signup and view all the answers

What is a regular polygon?

<p>A polygon that has all sides congruent and all angles congruent</p> Signup and view all the answers

What is a right angle?

<p>An angle that measures exactly 90°</p> Signup and view all the answers

What is a segment bisector?

<p>To separate something into two congruent parts</p> Signup and view all the answers

What is a side in geometry?

<p>The segments that form a closed figure</p> Signup and view all the answers

What is a sphere?

<p>The set of all points in space that are a given distance from a given point, called the center</p> Signup and view all the answers

What are supplementary angles?

<p>Two angles are supplementary if the sum of their measures is 180°</p> Signup and view all the answers

What is surface area?

<p>The sum of the areas of all the faces of a three-dimensional figure</p> Signup and view all the answers

What is a vertex?

<p>The common endpoint of the rays forming the angle</p> Signup and view all the answers

What are vertical angles?

<p>Opposite angles formed by the intersection of two lines</p> Signup and view all the answers

What is volume?

<p>The number of cubic units needed to fill the space occupied by a solid</p> Signup and view all the answers

What is an algebraic proof?

<p>An expression consisting of one or more numbers and variables along with one or more arithmetic operations</p> Signup and view all the answers

What is a conjecture?

<p>A conclusion reached that is based on inductive reasoning</p> Signup and view all the answers

What is a conjunction?

<p>A compound statement formed by joining two statements with the word and</p> Signup and view all the answers

What is a converse?

<p>The statement formed by exchanging the hypothesis and conclusion of a conditional statement</p> Signup and view all the answers

What is an inverse?

<p>The statement formed by negating both the hypothesis and conclusion of a conditional statement</p> Signup and view all the answers

What is a postulate?

<p>A rule of geometry that is accepted as being true without proof</p> Signup and view all the answers

What is a theorem?

<p>A statement that can be justified by logical reasoning and must be proven before it is accepted as true</p> Signup and view all the answers

What are parallel lines?

<p>Lines in the same plane that never intersect and have the same slope</p> Signup and view all the answers

What is point-slope form?

<p>An equation of the form y - y1 = m(x - x1), where m is the slope and (x1, y1) is a given point on a nonvertical line</p> Signup and view all the answers

What is rate of change?

<p>The change in a quantity over time</p> Signup and view all the answers

What are skew lines?

<p>Two nonparallel lines that do not intersect</p> Signup and view all the answers

What is slope?

<p>The ratio of the change in the y-coordinates (rise) to the corresponding change in the x-coordinates (run)</p> Signup and view all the answers

What is slope-intercept form?

<p>An equation of the form y = mx + b, where m is the slope and b is the y-intercept</p> Signup and view all the answers

What is a transversal?

<p>A line that intersects two or more other lines to form eight or more angles</p> Signup and view all the answers

What is an acute triangle?

<p>A triangle in which each angle measures less than 90°</p> Signup and view all the answers

What are base angles?

<p>The equal angles formed by the base and the congruent sides of an isosceles triangle</p> Signup and view all the answers

What are congruent polygons?

<p>Polygons that have the same shape and size</p> Signup and view all the answers

What are corresponding parts?

<p>Parts of congruent or similar figures that match</p> Signup and view all the answers

What is an equiangular triangle?

<p>A triangle with three congruent angles</p> Signup and view all the answers

What is an included angle?

<p>An angle formed by two given sides of a triangle</p> Signup and view all the answers

What is an included side?

<p>A side common to two given angles of a triangle</p> Signup and view all the answers

What is an isosceles triangle?

<p>A triangle with at least two congruent sides</p> Signup and view all the answers

What is a reflection in geometry?

<p>A transformation in which a figure is flipped over a line of symmetry</p> Signup and view all the answers

What is a right triangle?

<p>A triangle having one right angle</p> Signup and view all the answers

What is a rotation in geometry?

<p>A transformation in which a figure is turned around a fixed point</p> Signup and view all the answers

What is a scalene triangle?

<p>A triangle with no congruent sides</p> Signup and view all the answers

What is a translation in geometry?

<p>A transformation in which a figure is slid in any direction</p> Signup and view all the answers

What is an altitude?

<p>A line segment perpendicular to the base of a figure with endpoints on the base and on the vertex opposite the base</p> Signup and view all the answers

What is a centroid?

<p>The point of intersection of the three medians of a triangle</p> Signup and view all the answers

What is a circumcenter?

<p>The point of concurrency of the perpendicular bisectors of a triangle</p> Signup and view all the answers

What are concurrent lines?

<p>Three or more lines or segments that meet at a common point</p> Signup and view all the answers

What is an incenter?

<p>The point of concurrency of the angle bisectors of a triangle</p> Signup and view all the answers

What is a median in geometry?

<p>The middle number in a set of data when the data are arranged in numerical order</p> Signup and view all the answers

What is an orthocenter?

<p>The point of concurrency of the altitudes of a triangle</p> Signup and view all the answers

What is a perpendicular bisector?

<p>A segment that is perpendicular to another segment and passes through that segment's midpoint</p> Signup and view all the answers

What is a diagonal in geometry?

<p>A segment joining two nonconsecutive vertices of a polygon</p> Signup and view all the answers

What is an isosceles trapezoid?

<p>A trapezoid with two congruent legs</p> Signup and view all the answers

What is a kite in geometry?

<p>A quadrilateral with exactly two distinct pairs of adjacent congruent sides</p> Signup and view all the answers

What are legs in geometry?

<p>The sides of a right triangle that form the right angle</p> Signup and view all the answers

What is a midsegment of a trapezoid?

<p>A segment with endpoints that are the midpoints of two sides of a triangle</p> Signup and view all the answers

What is a parallelogram?

<p>A quadrilateral with both pairs of opposite sides parallel and congruent</p> Signup and view all the answers

What is a rectangle?

<p>A parallelogram with four right angles</p> Signup and view all the answers

What is a rhombus?

<p>A parallelogram with four congruent sides</p> Signup and view all the answers

Study Notes

Points and Lines

  • A point indicates a specific location without size or shape.
  • Line represents an endless straight path.
  • A line segment connects two endpoints.
  • Ray extends indefinitely in one direction from a fixed point.
  • Collinear points lie on the same line.

Angles

  • Angle is formed by two rays with a common endpoint.
  • Acute angle measures greater than 0° and less than 90°.
  • Obtuse angle measures more than 90° but less than 180°.
  • Right angle measures exactly 90°.
  • Complementary angles sum to 90°; supplementary angles sum to 180°.
  • Adjacent angles share a vertex and a common side without overlapping.
  • Vertical angles are opposite angles formed by intersecting lines.

Polygons and Triangles

  • A polygon is a closed figure with three or more sides formed by line segments.
  • A regular polygon has all sides and angles equal.
  • Equilateral triangle has three congruent sides; equiangular triangle has three congruent angles.
  • Isosceles triangle has at least two congruent sides; scalene triangle has no congruent sides.
  • Acute triangle has all angles less than 90°; right triangle contains one right angle; obtuse triangle has one angle greater than 90°.

Special Properties and Definitions

  • Circumference is the distance around a circle; perimeter is the total length of polygon sides.
  • Area measures the surface enclosed by a figure.
  • Volume quantifies the space occupied by a solid.
  • Surface area is the sum of all face areas of a 3D figure.
  • Base angles are the equal angles formed by the base of an isosceles triangle and its congruent sides.
  • Diagonal connects nonconsecutive vertices in a polygon.

3D Figures

  • A cone has a circular base and a vertex.
  • A cylinder consists of two congruent circular bases and a curved lateral surface.
  • A sphere is defined by all points equidistant from a center point.
  • A polyhedron has flat polygonal faces; regular polyhedron features regular congruent polygonal faces.
  • A pyramid has a polygon as its base and triangular faces converging to a vertex.

Relationships and Transformations

  • Parallel lines never intersect and have the same slope.
  • Perpendicular lines intersect to create right angles.
  • Transversal intersects two or more lines forming multiple angles.
  • Reflection flips a figure over a line of symmetry; rotation turns a figure around a point; translation slides a figure in any direction.

Special Terms

  • Vertex is the intersection point of two rays forming an angle.
  • Median is the middle value in a data set; the centroid is the intersection of a triangle's medians.
  • Orthocenter is the intersection of the altitudes of a triangle; circumcenter is where perpendicular bisectors meet.
  • Incenter is formed by the intersection of the angle bisectors of a triangle.

Logical Concepts

  • Postulate: accepted truth in geometry without proof.
  • Theorem: a statement that must be proven based on logical reasoning.
  • Conjecture: belief formed through inductive reasoning.
  • Conjunction joins two statements with "and"; inverse negates statements; converse switches hypothesis and conclusion in conditionals.

Miscellaneous

  • Rate of change describes how one quantity varies relative to another.
  • Skew lines are nonparallel lines that do not intersect.
  • Distance between two points measures straight-line space.

These definitions and properties are foundational for understanding geometric concepts and their applications in various mathematical contexts.

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Test your understanding of essential geometry terms with these flashcards. Each card presents a word commonly used in geometry along with its definition, helping you to reinforce your knowledge of the subject. Perfect for students preparing for geometry exams or for anyone looking to review basic concepts.

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