Count Vertices in a Geometric Figure: Identifying Points A through F

Vertex Identification with Labeled Points

How many vertices are shown in the figure?

AAABBBCCCDDDEEEFFF

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 How many perpendicular lines are in the drawing?
00:03 A perpendicular line is a line that forms a right angle at the intersection point with another line
00:11 Therefore all these lines are perpendicular
00:43 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

How many vertices are shown in the figure?

AAABBBCCCDDDEEEFFF

2

Step-by-step solution

Note that perpendicular lines are straight lines that create a right angle of 90 degrees at their intersection point.

Let's locate the intersection points that create the right angles in the drawing.

The lines that create the right angles are:

AB is perpendicular to BC

BC is perpendicular to CD

CD is perpendicular to DA

DA is perpendicular to AB

BC is perpendicular to EF

AD is perpendicular to EF

Therefore, in the drawing there are 6 perpendicular lines.

3

Final Answer

6

Key Points to Remember

Essential concepts to master this topic
  • Definition: A vertex is a corner point where two or more lines meet
  • Technique: Count each labeled point: A, B, C, D, E, F = 6 vertices
  • Check: Verify each point connects at least two line segments together ✓

Common Mistakes

Avoid these frequent errors
  • Counting intersection points without labels
    Don't count every line intersection you see = wrong total! Some intersections aren't vertices of the main figure. Always count only the clearly labeled points (A, B, C, D, E, F) that form the geometric figure.

Practice Quiz

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What do the four figures below have in common?

1234

FAQ

Everything you need to know about this question

What exactly is a vertex in geometry?

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A vertex is a corner point where two or more line segments meet. Think of it as a sharp corner on a shape - like the corners of a square or triangle.

Do I count all the points I see in the figure?

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No! Only count the labeled points (A, B, C, D, E, F). These are the actual vertices of the geometric figure. Other intersection points are just where construction lines cross.

Why are there small squares at some corners?

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Those small squares indicate right angles (90°). They help you understand the shape better, but don't change the vertex count - you still count each labeled corner point once.

How can I be sure I counted all vertices correctly?

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List each labeled point systematically: A, B, C, D, E, F. That's 6 vertices total. Double-check by going around the figure in order!

What if some points look like they're in the middle of lines?

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Points E and F appear on the horizontal line, but they're still vertices because they're labeled and connect multiple line segments. Count all labeled points regardless of position.

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