Theorems for Parallel Lines and Perpendicular Lines

Which of the following proves the given example?

• Theorem of Perpendicular and Parallel Lines

• Corresponding Angle Converse

• Parallel Lines Theorem

• Definition of Parallel Lines

Answer explanation

The Theorem of Perpendicular and Parallel Lines states that if 2 lines are perpendicular to the same line, they are parallel. In the example, the 2 horizontal lines are perpendicular to the same vertical line. Therefore, they are parallel.

Which of the following can help you prove that

l || m using the example given?

• Theorem of Perpendicular and Parallel Lines

• Corresponding Angle Converse

• Parallel Lines Theorem

• Definition of Parallel Lines

Answer explanation

According to the Corresponding Angle Converse, if 2 lines are cut by a transversal and corresponding angles are congruent, it follows that the 2 lines are parallel.

Which of the following can help you prove that p || r?

• Theorem of Perpendicular and Parallel Lines

• Parallel Lines Theorem

• Transitive Property of Parallel Lines

Answer explanation

The transitive property of parallel lines states that if 2 lines are parallel to the same line, they are parallel to each other.

Prove that l1 || l3.

What theorem/postulate/definition/converse/property can help you prove that l1 || l3?

Answer explanation

According to the Transitive Property of Parallel Lines, if 2 lines are parallel to the same line, they are parallel to each other.

Which of the following statements can prove that lines and segments are parallel?

• Same-side interior angles are parallel

• Alternate exterior angles are congruent

• Alternate exterior angles are corresponding

• Corresponding angles are supplementary

Which of the following statements can prove that lines and segments are perpendicular?

• Lines are perpendicular to the same line

• Same-side interior angles are congruent

• Same-side exterior angles are congruent

• A line is perpendicular to one of the two parallel lines