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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