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Questions and Answers
What is the term for the corners of a shape?
What is the term for shapes that are the same size and shape?
What is the term for the horizontal axis of the coordinate plane?
What is the term for a set of outcomes of an experiment?
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What type of probability is based on the results of repeated experiments?
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What is the term for a point on the coordinate plane represented as (x, y)?
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Which geometric term describes a set of points that extend infinitely in two directions?
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What is the unit of measurement where 1 radian equals $\frac{180°}{π}$?
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Which type of angle is exactly 180 degrees?
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Which formula is used to calculate the distance between two points $(x1, y1)$ and $(x2, y2)$?
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What is the midpoint of a line segment?
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Which of the following is a common endpoint where two rays meet to form an angle?
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Study Notes
Points And Lines
- Point: a location in space represented by a set of coordinates (x, y, z)
- Line: a set of points that extend infinitely in two directions
- Line segment: a part of a line with a fixed length
- Ray: a line that extends infinitely in one direction from a point
- Midpoint: the point that divides a line segment into two equal parts
- Distance formula: used to calculate the distance between two points (x1, y1) and (x2, y2): √((x2 - x1)^2 + (y2 - y1)^2)
Angles And Measurements
- Angle: formed by two rays sharing a common endpoint (vertex)
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Types of angles:
- Acute angle: less than 90°
- Right angle: exactly 90°
- Obtuse angle: greater than 90° but less than 180°
- Straight angle: exactly 180°
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Angle measurements:
- Degrees: a unit of measurement for angles (1° = 1/360 of a circle)
- Radians: a unit of measurement for angles (1 rad = 180°/π)
Shapes And Figures
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Types of shapes:
- 2D shapes: flat shapes with no thickness (e.g. triangles, quadrilaterals, polygons)
- 3D shapes: solid shapes with thickness (e.g. pyramids, prisms, spheres)
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Properties of shapes:
- Vertices: corners of a shape
- Edges: sides of a shape
- Faces: surfaces of a shape
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Types of figures:
- Congruent figures: identical shapes and sizes
- Similar figures: same shape but different sizes
Coordinate Geometry
- Coordinate plane: a grid system used to graph points and shapes
- X-axis: the horizontal axis of the coordinate plane
- Y-axis: the vertical axis of the coordinate plane
- Ordered pairs: used to represent points on the coordinate plane (x, y)
- Graphing shapes: used to visualize and analyze shapes and figures
Probability
- Experiment: an action or situation that can produce a set of outcomes
- Outcome: a possible result of an experiment
- Sample space: the set of all possible outcomes of an experiment
- Event: a set of outcomes of an experiment
- Probability of an event: a number between 0 and 1 that represents the likelihood of an event occurring
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Types of probability:
- Theoretical probability: based on the number of favorable outcomes and the total number of outcomes
- Experimental probability: based on the results of repeated experiments
Points And Lines
- A point is a location in space represented by a set of coordinates (x, y, z)
- A line is a set of points that extend infinitely in two directions
- A line segment is a part of a line with a fixed length
- A ray is a line that extends infinitely in one direction from a point
- The midpoint is the point that divides a line segment into two equal parts
- The distance formula calculates the distance between two points (x1, y1) and (x2, y2): √((x2 - x1)^2 + (y2 - y1)^2)
Angles And Measurements
- An angle is formed by two rays sharing a common endpoint (vertex)
- Acute angles are less than 90°
- Right angles are exactly 90°
- Obtuse angles are greater than 90° but less than 180°
- Straight angles are exactly 180°
- Angles can be measured in degrees, with 1° equal to 1/360 of a circle
- Angles can also be measured in radians, with 1 rad equal to 180°/π
Shapes And Figures
- 2D shapes are flat shapes with no thickness
- 3D shapes are solid shapes with thickness
- Shapes have vertices (corners), edges (sides), and faces (surfaces)
- Congruent figures are identical in shape and size
- Similar figures are the same shape but different sizes
Coordinate Geometry
- The coordinate plane is a grid system used to graph points and shapes
- The x-axis is the horizontal axis of the coordinate plane
- The y-axis is the vertical axis of the coordinate plane
- Ordered pairs (x, y) are used to represent points on the coordinate plane
- Graphing shapes helps visualize and analyze shapes and figures
Probability
- An experiment is an action or situation that can produce a set of outcomes
- An outcome is a possible result of an experiment
- The sample space is the set of all possible outcomes of an experiment
- An event is a set of outcomes of an experiment
- Probability of an event is a number between 0 and 1 that represents the likelihood of an event occurring
- Theoretical probability is based on the number of favorable outcomes and the total number of outcomes
- Experimental probability is based on the results of repeated experiments
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Description
Learn the fundamentals of points, lines, and line segments in geometry. Learn how to calculate the distance between two points using the distance formula.
