Perpendicular Line Identification in Rectangle with Parallel Lines

Q: How do I tell if two lines are perpendicular just by looking?

Look for right angle markers (small squares) at intersection points! In rectangles, all corners are automatically 90-degree angles, so any two lines meeting at a corner are perpendicular.

Q: Why do I get 8 pairs instead of 4 corners?

Each corner has two additional lines running through it! The rectangle has 4 corners, but the vertical lines EF and GH create 4 more intersection points with perpendicular horizontal lines.

Q: Do parallel lines count as perpendicular?

No! Parallel lines never intersect, so they can't form right angles. Only count lines that actually cross each other at 90-degree angles.

Q: What if the lines extend beyond the rectangle?

It doesn't matter! Perpendicular lines remain perpendicular no matter how long they are. Focus on where the lines intersect and whether they form right angles at those points.

Q: How do I systematically count all pairs without missing any?

Go through each intersection point one by one. At each point, identify the two lines crossing and check if they form a 90-degree angle. This gives you exactly 8 intersection points with perpendicular lines.

Perpendicular Lines with Rectangle Intersection Points

How many pairs of perpendicular lines are shown in the diagram?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 How many perpendiculars are there in the drawing?

00:04 A perpendicular creates a right angle at the intersection point between the lines

00:10 Let's mark and count all the right angles

00:39 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

How many pairs of perpendicular lines are shown in the diagram?

Step-by-step solution

Remember that perpendicular lines are lines that form a right angle of 90 degrees between them.

We will draw straight lines coming from each of the marked points in the figure to examine whether the angles are right angles.

The drawing will look like this:

Note that the lines we drew create right angles, which are:

$BAD,ABC,BCD,CDA,GEF,EGH,GHF,HFE$

The lines that form angle BAD are: BA+AD

The lines that form angle ABC are: AB+BC

The lines that form angle BCD are: BC+CD

The lines that form angle CDA are: CD+DA

The lines that form angle GEF are: GE+EF

The lines that form angle EGH are: EG+GH

The lines that form angle GHF are: GH+HF

The lines that form angle HFE are: HF+FE

Given that in the drawing we have 8 angles of 90 degrees marked, we must have 8 pairs of perpendicular lines.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: Perpendicular lines meet at exactly 90-degree right angles
Technique: Count each corner's right angle = 2 intersecting lines forming 1 pair
Check: Draw right angle markers at each vertex to verify 8 pairs ✓

Common Mistakes

Avoid these frequent errors

Counting angles instead of line pairs
Don't count 8 angles and think that's the answer = missing the actual pairs! Each right angle is formed by exactly 2 perpendicular lines working together. Always count the pairs of lines that create each 90-degree angle.

Practice Quiz

Test your knowledge with interactive questions

Determine which lines are parallel to one another?

FAQ

Everything you need to know about this question

How do I tell if two lines are perpendicular just by looking?

Look for right angle markers (small squares) at intersection points! In rectangles, all corners are automatically 90-degree angles, so any two lines meeting at a corner are perpendicular.

Why do I get 8 pairs instead of 4 corners?

Each corner has two additional lines running through it! The rectangle has 4 corners, but the vertical lines EF and GH create 4 more intersection points with perpendicular horizontal lines.

Do parallel lines count as perpendicular?

No! Parallel lines never intersect, so they can't form right angles. Only count lines that actually cross each other at 90-degree angles.

What if the lines extend beyond the rectangle?

It doesn't matter! Perpendicular lines remain perpendicular no matter how long they are. Focus on where the lines intersect and whether they form right angles at those points.

How do I systematically count all pairs without missing any?

Go through each intersection point one by one. At each point, identify the two lines crossing and check if they form a 90-degree angle. This gives you exactly 8 intersection points with perpendicular lines.

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