Perpendicular lines are vertical lines that form a right angle between them, that is, an angle of degrees.
Perpendicular lines appear in many geometric shapes, such as a rectangle, a square, a right triangle, and others.
Perpendicular Lines Practice Problems & Worksheets
Master perpendicular lines with interactive practice problems. Learn to identify right angles, solve geometry problems, and apply concepts in rectangles and triangles.
📚Master Perpendicular Lines with Step-by-Step Practice
- Identify perpendicular lines that form 90-degree right angles
- Recognize perpendicular lines in rectangles, squares, and right triangles
- Solve problems involving perpendicular line relationships in geometric shapes
- Apply perpendicular line concepts to real-world geometric situations
- Distinguish between perpendicular and parallel lines in various contexts
- Calculate angles formed by perpendicular intersections
Understanding Perpendicular Lines
Complete explanation with examples
Practice Perpendicular Lines
Test your knowledge with 10 quizzes
What do the four figures have in common?
Examples with solutions for Perpendicular Lines
Step-by-step solutions included
Exercise #1
What do the four figures below have in common?
Step-by-Step Solution
Let's think about the different definitions of different lines.
Let's remember that parallel lines are lines that will never intersect with each other.
We can see that what's common to all the lines in the drawings is that if we extend them, we won't be able to find an intersection point, meaning they will never meet.
Therefore, the correct answer is b.
Answer:
All parallel
Video Solution
Exercise #2
What do the four figures have in common?
Step-by-Step Solution
Remember that perpendicular lines form a 90-degree angle between them.
Parallel lines are lines that never intersect and do not form any angle between them.
To be able to examine the lines, a line will be drawn at each end of the line, as follows:
We notice that from the drawings it seems that all the lines do not form any angle between them, this is because they do not meet each other.
Therefore, all figures show parallel lines.
Answer:
All show parallel lines.
Video Solution
Exercise #3
Which lines are perpendicular to each other?
Step-by-Step Solution
Let's remember that perpendicular lines are lines that form an angle of 90 degrees between them.
In each of the answers, we will draw the letter T at the point of intersection of the lines.
Let's examine figure A:
We notice that the lines do form a right angle and the lines are perpendicular to each other.
Let's examine figure B:
We notice that the lines do not meet and do not form any angle; therefore, they are parallel lines and not perpendicular.
Answer:
Video Solution
Exercise #4
Which of the lines are perpendicular to each other?
Step-by-Step Solution
Let's remember that perpendicular lines are lines that form a right angle of 90 degrees between them.
In each of the answers, we will draw the letter T at the point of intersection of the lines.
Let's examine figure A:
We will notice that the lines do not form a right angle, and therefore are not perpendicular.
Let's examine figure B:
The lines do indeed form a 90-degree angle and are therefore perpendicular.
Let's examine figure C:
We notice that the lines do not form a right angle, and therefore are not perpendicular.
Answer:
Video Solution
Exercise #5
Which lines are perpendicular to each other?
Step-by-Step Solution
Perpendicular lines are lines that form a right angle of 90 degrees between them.
The only drawing where the lines form a right angle of 90 degrees between them is drawing A.
Answer:
Video Solution
Frequently Asked Questions
What are perpendicular lines in geometry?
+Perpendicular lines are two lines that intersect to form a right angle of exactly 90 degrees. They are commonly found in geometric shapes like rectangles, squares, and right triangles where adjacent sides meet at right angles.
How do you identify perpendicular lines in a rectangle?
+In a rectangle, all adjacent sides are perpendicular to each other. This means: 1) The length and width meet at 90°, 2) All four corners are right angles, 3) Any two connecting sides form perpendicular lines.
What is the difference between perpendicular and parallel lines?
+Perpendicular lines intersect at 90-degree angles, while parallel lines never intersect and maintain the same distance apart. Perpendicular lines cross each other, but parallel lines run alongside each other indefinitely.
Where do we see perpendicular lines in real life?
+Common examples include: corner of a book or paper, intersection of walls and floors, street corners at right angles, window frames, and the corners of rectangular objects like phones or tablets.
How do perpendicular lines appear in right triangles?
+In a right triangle, the two sides that form the right angle (90°) are perpendicular to each other. These are called the legs of the triangle, and they meet at the vertex opposite to the hypotenuse.
What symbol is used to show perpendicular lines?
+The symbol ⊥ is used to indicate perpendicular lines. For example, if line AB is perpendicular to line CD, we write AB ⊥ CD. This symbol represents the 90-degree angle formed at their intersection.
Can perpendicular lines be vertical and horizontal?
+Yes, when one line is perfectly vertical and another is perfectly horizontal, they are perpendicular. This creates the classic 90-degree angle, like the intersection of the x-axis and y-axis on a coordinate plane.
How do you solve perpendicular lines problems in geometry?
+To solve perpendicular lines problems: 1) Look for right angle markers (small squares), 2) Use the fact that perpendicular angles equal 90°, 3) Apply properties of rectangles and squares, 4) Remember that adjacent sides in rectangles are always perpendicular.