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?
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What are undefined terms in geometry?
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What is an acute angle?
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What are adjacent angles?
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What is an angle?
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What is an angle bisector?
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What is area in geometry?
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What is a base in geometry?
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What does it mean for a point to be 'between' in geometry?
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What does collinear mean?
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What are complementary angles?
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What does concave mean in terms of polygons?
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What is a cone in geometry?
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What does congruent mean?
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What is construction in geometry?
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What does convex mean?
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What is a cylinder?
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What is a degree?
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What does distance refer to in geometry?
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What is an edge in geometry?
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What is an equilateral polygon?
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What is an equiangular polygon?
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What does exterior mean in terms of angles?
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What is the face of a figure?
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What does interior mean in terms of angles?
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What is the intersection in geometry?
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What is a line in geometry?
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What is a linear pair?
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What is a line segment?
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What is a midpoint?
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What is an n-gon?
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What is an obtuse angle?
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What are opposite rays?
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What does perpendicular mean?
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What is a plane in geometry?
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What is a polygon?
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What is a polyhedron?
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What is a prism?
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What is a pyramid?
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What is a ray?
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What is a regular polygon?
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What is a right angle?
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What is a segment bisector?
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What is a side in geometry?
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What is a sphere?
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What are supplementary angles?
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What is surface area?
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What is a vertex?
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What are vertical angles?
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What is volume?
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What is an algebraic proof?
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What is a conjecture?
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What is a conjunction?
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What is a converse?
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What is an inverse?
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What is a postulate?
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What is a theorem?
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What are parallel lines?
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What is point-slope form?
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What is rate of change?
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What are skew lines?
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What is slope?
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What is slope-intercept form?
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What is a transversal?
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What is an acute triangle?
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What are base angles?
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What are congruent polygons?
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What are corresponding parts?
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What is an equiangular triangle?
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What is an included angle?
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What is an included side?
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What is an isosceles triangle?
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What is a reflection in geometry?
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What is a right triangle?
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What is a rotation in geometry?
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What is a scalene triangle?
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What is a translation in geometry?
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What is an altitude?
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What is a centroid?
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What is a circumcenter?
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What are concurrent lines?
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What is an incenter?
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What is a median in geometry?
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What is an orthocenter?
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What is a perpendicular bisector?
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What is a diagonal in geometry?
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What is an isosceles trapezoid?
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What is a kite in geometry?
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What are legs in geometry?
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What is a midsegment of a trapezoid?
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What is a parallelogram?
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What is a rectangle?
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What is a rhombus?
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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.