Question

1. determine whether each statement is always, sometimes, or never true. categorize them accordingly.

two lines in the same plane are parallel.
two lines in intersecting planes are perpendicular.
perpendicular lines meet at right angles.
two lines in parallel planes are perpendicular.

Explanation:

Step1: Analyze "Two lines in the same plane are parallel"

Two lines in the same plane can either be parallel or intersect. So, this statement is not always true.

Step2: Analyze "Two lines in intersecting planes are perpendicular"

Two lines in intersecting planes may or may not be perpendicular. There is no guarantee.

Step3: Analyze "Perpendicular lines meet at right angles"

By the definition of perpendicular lines, they always meet at right angles.

Step4: Analyze "Two lines in parallel planes are perpendicular"

Two lines in parallel planes may or may not be perpendicular.

Answer:

• "Two lines in the same plane are parallel": Sometimes
• "Two lines in intersecting planes are perpendicular": Sometimes
• "Perpendicular lines meet at right angles": Always
• "Two lines in parallel planes are perpendicular": Sometimes