Geometry Chapter 3 Quiz Flashcards

What are parallel lines?

What are skew lines?

What is a transversal?

If a transversal intersects two parallel lines, then corresponding angles are congruent.

If a transversal intersects two parallel lines, then alternate interior angles are congruent.

If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.

If two lines are perpendicular, then they form right angles.

What does Theorem 3.1 state?

What does Theorem 3.2 state?

If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.

If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel.

If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel.

What does Theorem 3.11 state?

What does Theorem 3.12 state?

Parallel and Skew Lines

Parallel lines are coplanar and do not intersect.
Skew lines are non-coplanar and do not intersect or run parallel.

Transversal

A transversal is defined as a line, ray, or segment that crosses two or more lines, rays, or segments at different points.

Angle Relationships

The Corresponding Angles Postulate states that corresponding angles formed by a transversal intersecting two parallel lines are congruent.
The Alternate Interior Angles Theorem asserts that alternate interior angles formed in the same scenario are also congruent.
The Alternate Exterior Angles Theorem indicates that pairs of alternate exterior angles created by a transversal cutting parallel lines are congruent.
The Same-Side Interior Angles Theorem declares that same-side interior angles are supplementary when a transversal intersects parallel lines.

Perpendicular Lines

Perpendicular lines intersect at right angles.
The theorem states that if two lines create a linear pair of congruent angles, the lines are perpendicular (Theorem 3.1).
Additionally, if the sides of two adjacent acute angles are perpendicular, then those angles are complementary (Theorem 3.2).

Converse Statements and Parallel Lines

The Corresponding Angles Postulate Converse claims that if corresponding angles are congruent when lines are intersected by a transversal, the lines are parallel.
The Alternate Interior Angles Theorem Converse indicates that congruent alternate interior angles imply the lines are parallel.
The Alternate Exterior Angles Theorem Converse similarly states that congruent alternate exterior angles imply the lines are parallel.
Theorem 3.11 explains that if two lines are parallel to the same line, they are parallel to each other.
Theorem 3.12 proclaims that if two lines are perpendicular to the same line, they are parallel to each other.

Test your understanding of key geometry concepts from Chapter 3 with these flashcards. This quiz covers important definitions including parallel lines, skew lines, transversals, and corresponding angles. Perfect for reinforcing your geometry knowledge!