Geometry: Parallel and Perpendicular Lines

Questions and Answers

What are parallel lines?

Two lines that intersect

Two lines that lie on the same plane and have no points in common (correct)

Two lines that create a 90 degree angle

Two lines that have the same slope

What are perpendicular lines?

Two lines that intersect and create a 90 degree angle

What is slope?

The ratio of rise to run for any two exact points on the line

What is rise in relation to a line?

The difference in the y-values of two exact points on a line Signup and view all the answers

What is run in relation to a line?

The difference in the x-values of two exact points on a line Signup and view all the answers

What characterizes a negative slope?

When the slope of a line falls from the left side of the graph to the right side of the graph Signup and view all the answers

What characterizes a positive slope?

When the slope of a line rises from the left side of the graph to the right side of the graph Signup and view all the answers

What is meant by no slope?

When a line has no slope, it is identified as a horizontal line Signup and view all the answers

What does undefined slope refer to?

When a line is undefined, it is identified as a vertical line Signup and view all the answers

Study Notes

Concepts of Parallel and Perpendicular Lines

Parallel Lines: Do not intersect and exist on the same plane, ensuring they maintain a constant distance apart.
Perpendicular Lines: Intersect at a right angle (90 degrees), indicating a specific relationship between their slopes.

Understanding Slope

Slope: Represents the steepness of a line and is calculated as the ratio of the 'rise' (vertical change) to the 'run' (horizontal change).
Rise: The change in the y-values between two points on the line, essential for determining the slope's value.
Run: The change in the x-values between two points on the line, also crucial for slope calculation.

Types of Slopes

Negative Slope: Indicates a line that descends from left to right, suggesting a decrease in y-values as x-values increase.
Positive Slope: Denotes a line that ascends from left to right, signifying an increase in y-values with an increase in x-values.
No Slope: Characterizes horizontal lines where the y-value remains constant, leading to a slope of zero.
Undefined Slope: Describes vertical lines where the x-value remains constant; this slope is considered undefined due to the vertical rise over a horizontal run of zero.

Description

This quiz covers the essential concepts of parallel and perpendicular lines, including their definitions and slopes. You'll explore the characteristics of different slope types and how they relate to line orientation in a plane. Test your understanding of these fundamental geometric principles.