Videos, examples, solutions, and lessons to help High School students know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point,line, distance along a line, and distance around a circular arc.

Common Core: HSG-CO.A.1

**Geometry: Some Precise Definitions**

CC.9-12.G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

Parallel lines - Two coplanar lines m and n are parallel lines, written m || n, if and only if they have no points in common or they are identical.

Line segment - The line segment with endpoints A and B, denoted AB, is the set consisting of the distinct points A and B and all points between A and B.

Angle - An angle is the union of two rays or line segments that have the same endpoint.

**Geometry Vocabulary**

G.CO.1: Know precise definitions of angle, circle, perpendicular line, parallel line, line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

**Introduction to Geometry**

Point, Line, Plane, Segment, Ray, Angle, Collinear, Coplanar. Point - A point represents a location in space (Usually us an upper case letter)

Line - A line is determined by 2 points.

Ray - A ray is a part of a line starting at one point and extending in only one direction.

Angle - An angle is formed by two rays extending out of the same point.

Collinear - Two points are collinear if they are on the same line.

Plane - A plane is determined by 3 points.

**Point, Line, Plane Examples**

**Parallel, Intersecting, Perpendicular Lines**

What happens when lines cross?**How do you find the distance between two points?**

Explain how to obtain the distance formula.

Examples:

The distance between two points is 9. One of the points is (5,1) and the other point is at x = -4. What is the y value for x = -4?

**How to define a circle?**

Equation of a circle: (x-h)^{2} + (y-k)^{2} = r^{2}

**Degrees, Radians, and Arc Length**

This video demonstrates how to convert from degrees to radians and from radians to degrees. Also, use of the arc length formula is shown and problems worked to find an unknown arc length, an unknown angle, and an unknown radius.

2π radians = 360 degrees

1 radian = 180/π degrees

1 degree = π/180 radians

Example:

How many radians are 45 degrees?

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Common Core: HSG-CO.A.1

Related Topics:

Common
Core (Geometry)

Common Core
for Mathematics

CC.9-12.G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

Parallel lines - Two coplanar lines m and n are parallel lines, written m || n, if and only if they have no points in common or they are identical.

Line segment - The line segment with endpoints A and B, denoted AB, is the set consisting of the distinct points A and B and all points between A and B.

Angle - An angle is the union of two rays or line segments that have the same endpoint.

G.CO.1: Know precise definitions of angle, circle, perpendicular line, parallel line, line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

Point, Line, Plane, Segment, Ray, Angle, Collinear, Coplanar. Point - A point represents a location in space (Usually us an upper case letter)

Line - A line is determined by 2 points.

Ray - A ray is a part of a line starting at one point and extending in only one direction.

Angle - An angle is formed by two rays extending out of the same point.

Collinear - Two points are collinear if they are on the same line.

Plane - A plane is determined by 3 points.

What happens when lines cross?

Explain how to obtain the distance formula.

Examples:

The distance between two points is 9. One of the points is (5,1) and the other point is at x = -4. What is the y value for x = -4?

Equation of a circle: (x-h)

This video demonstrates how to convert from degrees to radians and from radians to degrees. Also, use of the arc length formula is shown and problems worked to find an unknown arc length, an unknown angle, and an unknown radius.

2π radians = 360 degrees

1 radian = 180/π degrees

1 degree = π/180 radians

Example:

How many radians are 45 degrees?

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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