Perpendicular and Parallel Lines
Perpendicular lines cross at a right angle of exactly 90°. Where they meet, they form a square corner, like the corner of a book. Parallel lines stay the same distance apart and never meet.
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What are Different Types of Lines?
- A line segment has two endpoints, a ray has one endpoint, and a line has no endpoints.
- Rays and lines continue forever, but a line segment has a fixed length.
What are Perpendicular and Parallel Lines?
- Perpendicular lines meet at a right angle ().
- Parallel lines stay the same distance apart and never meet.
How to Measure Distance Between Points and Lines
- The distance between two points is the length of the line segment joining them.
- The distance between parallel lines is the length of the perpendicular line segment between them.
Practice Questions
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What do we call a straight line with two distinct endpoints?
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A straight line with two distinct endpoints is called a line segment, as it has a definite start and end.
Which of these lines never intersect and stay the same distance apart?
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Parallel lines never intersect and remain the same distance apart, unlike perpendicular lines, which intersect at right angles.
Two parallel lines are apart. A perpendicular line segment is drawn between them. What is the length of this line segment?
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The perpendicular line segment between two parallel lines is the same as the distance between them, which is .
If you draw two lines that are perpendicular, what kind of angle do they form?
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When two lines are perpendicular, they meet at a right angle, which measures exactly .
If two lines are parallel, what is true about the distance between them?
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The distance between parallel lines is constant and never changes. This is one of their defining properties.
What is the shortest distance from a point to a line?
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The shortest distance from a point to a line is always a perpendicular line segment drawn from the point to the line.
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Students Also Ask
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A line segment has two endpoints and a fixed length you can measure. A ray has one endpoint and extends forever in one direction. A line has no endpoints and extends forever in both directions. All three are perfectly straight.
Perpendicular lines meet at a single point, and they always cross there at a right angle of exactly 90°. This stays true whatever their orientation, so it does not matter how you rotate the pair. The right angle is what makes the lines perpendicular.
Perpendicular lines use the symbol ⊥. So line a ⊥ line b means the two lines cross at a right angle. Parallel lines use the symbol ∥. So line a ∥ line b means the two lines stay the same distance apart and never meet.
No. Parallel lines never meet, however far you extend them in either direction. They stay exactly the same distance apart all the way along, which is why they never cross. This holds whatever their orientation, so the angle of the pair does not change it.
No. Orientation does not matter for either relationship. Perpendicular lines stay perpendicular as long as they cross at 90°, no matter how you rotate them. Parallel lines stay parallel as long as they keep the same distance apart, at any angle.
The shortest distance from a point to a line is measured along the perpendicular from the point to the line. You draw a line from the point that meets the line at a right angle of 90°. Then measure that perpendicular segment. This perpendicular gives the shortest distance.