Podcast
Questions and Answers
What is the definition of 'point'?
What is the circumference?
The distance around a circle
What does coplanar mean?
Points that lie on the same plane
What is perimeter?
Signup and view all the answers
What are undefined terms in geometry?
Signup and view all the answers
What is an acute angle?
Signup and view all the answers
What are adjacent angles?
Signup and view all the answers
What is an angle?
Signup and view all the answers
What is an angle bisector?
Signup and view all the answers
What is area in geometry?
Signup and view all the answers
What is a base in geometry?
Signup and view all the answers
What does it mean for a point to be 'between' in geometry?
Signup and view all the answers
What does collinear mean?
Signup and view all the answers
What are complementary angles?
Signup and view all the answers
What does concave mean in terms of polygons?
Signup and view all the answers
What is a cone in geometry?
Signup and view all the answers
What does congruent mean?
Signup and view all the answers
What is construction in geometry?
Signup and view all the answers
What does convex mean?
Signup and view all the answers
What is a cylinder?
Signup and view all the answers
What is a degree?
Signup and view all the answers
What does distance refer to in geometry?
Signup and view all the answers
What is an edge in geometry?
Signup and view all the answers
What is an equilateral polygon?
Signup and view all the answers
What is an equiangular polygon?
Signup and view all the answers
What does exterior mean in terms of angles?
Signup and view all the answers
What is the face of a figure?
Signup and view all the answers
What does interior mean in terms of angles?
Signup and view all the answers
What is the intersection in geometry?
Signup and view all the answers
What is a line in geometry?
Signup and view all the answers
What is a linear pair?
Signup and view all the answers
What is a line segment?
Signup and view all the answers
What is a midpoint?
Signup and view all the answers
What is an n-gon?
Signup and view all the answers
What is an obtuse angle?
Signup and view all the answers
What are opposite rays?
Signup and view all the answers
What does perpendicular mean?
Signup and view all the answers
What is a plane in geometry?
Signup and view all the answers
What is a polygon?
Signup and view all the answers
What is a polyhedron?
Signup and view all the answers
What is a prism?
Signup and view all the answers
What is a pyramid?
Signup and view all the answers
What is a ray?
Signup and view all the answers
What is a regular polygon?
Signup and view all the answers
What is a right angle?
Signup and view all the answers
What is a segment bisector?
Signup and view all the answers
What is a side in geometry?
Signup and view all the answers
What is a sphere?
Signup and view all the answers
What are supplementary angles?
Signup and view all the answers
What is surface area?
Signup and view all the answers
What is a vertex?
Signup and view all the answers
What are vertical angles?
Signup and view all the answers
What is volume?
Signup and view all the answers
What is an algebraic proof?
Signup and view all the answers
What is a conjecture?
Signup and view all the answers
What is a conjunction?
Signup and view all the answers
What is a converse?
Signup and view all the answers
What is an inverse?
Signup and view all the answers
What is a postulate?
Signup and view all the answers
What is a theorem?
Signup and view all the answers
What are parallel lines?
Signup and view all the answers
What is point-slope form?
Signup and view all the answers
What is rate of change?
Signup and view all the answers
What are skew lines?
Signup and view all the answers
What is slope?
Signup and view all the answers
What is slope-intercept form?
Signup and view all the answers
What is a transversal?
Signup and view all the answers
What is an acute triangle?
Signup and view all the answers
What are base angles?
Signup and view all the answers
What are congruent polygons?
Signup and view all the answers
What are corresponding parts?
Signup and view all the answers
What is an equiangular triangle?
Signup and view all the answers
What is an included angle?
Signup and view all the answers
What is an included side?
Signup and view all the answers
What is an isosceles triangle?
Signup and view all the answers
What is a reflection in geometry?
Signup and view all the answers
What is a right triangle?
Signup and view all the answers
What is a rotation in geometry?
Signup and view all the answers
What is a scalene triangle?
Signup and view all the answers
What is a translation in geometry?
Signup and view all the answers
What is an altitude?
Signup and view all the answers
What is a centroid?
Signup and view all the answers
What is a circumcenter?
Signup and view all the answers
What are concurrent lines?
Signup and view all the answers
What is an incenter?
Signup and view all the answers
What is a median in geometry?
Signup and view all the answers
What is an orthocenter?
Signup and view all the answers
What is a perpendicular bisector?
Signup and view all the answers
What is a diagonal in geometry?
Signup and view all the answers
What is an isosceles trapezoid?
Signup and view all the answers
What is a kite in geometry?
Signup and view all the answers
What are legs in geometry?
Signup and view all the answers
What is a midsegment of a trapezoid?
Signup and view all the answers
What is a parallelogram?
Signup and view all the answers
What is a rectangle?
Signup and view all the answers
What is a rhombus?
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
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.