Geometry: Parallel and Perpendicular Lines

These flashcards cover key concepts from Chapter 3 on parallel and perpendicular lines in Geometry, including definitions, theorems, proofs, and equations.

What are the key relationships explored in Chapter 3 of Geometry?

The key relationships explored are parallel and perpendicular lines.

What is a transversal in geometry?

A transversal is a line that intersects two or more lines in a plane.

What theorem can be used to prove that two lines are parallel?

Theorems such as the Corresponding Angles Postulate can be used to prove that two lines are parallel.

How can one find the measures of angles so that lines are parallel?

By using algebraic methods and theorems related to angle relationships.

What is the purpose of using proofs in geometry?

To provide logical arguments to demonstrate that certain statements about lines are true.

What theorem relates to angles formed by parallel lines cut by a transversal?

The Alternate Interior Angles Theorem states that alternate interior angles are equal.

How do you construct parallel lines?

By using a ruler and compass or by applying geometric constructions methods.

What is the slope of a line?

The slope of a line is a measure of its steepness, defined as the change in y over the change in x.

What form is used to write the equation of a line?

The slope-intercept form, which is written as y = mx + b.

What is the significance of comparing slopes of lines?

Lines with equal slopes are parallel, while lines with slopes that are negative reciprocals are perpendicular.