Count the Vertices: Identifying Points A through J in a Geometric Figure

Vertex Identification with Geometric Intersections

How many vertices are shown in the figure?

CCCDDDEEEFFFAAABBBIIIJJJGGGHHH

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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 creates a right angle at its intersection point with another line
00:07 Therefore all these lines are perpendicular
00:21 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?

CCCDDDEEEFFFAAABBBIIIJJJGGGHHH

2

Step-by-step solution

Note that perpendicular lines are straight lines that create a 90-degree angle at their intersection point.

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

CCCDDDEEEFFFAAABBBIIIJJJGGGHHH

The lines that create the marked right angles are:

AB is perpendicular to CD

AB is perpendicular to EF

EF is perpendicular to IJ

IJ is perpendicular to GH

Therefore, there are 4 perpendicular lines in the drawing.

3

Final Answer

5

Key Points to Remember

Essential concepts to master this topic
  • Definition: A vertex is where two or more lines meet to form an angle
  • Technique: Count intersection points marked with squares: 5 vertices total
  • Check: Verify each labeled point A through J creates line intersections ✓

Common Mistakes

Avoid these frequent errors
  • Counting all labeled points as vertices
    Don't count every point A through J as a vertex = 10 wrong answer! Points on lines without intersections aren't vertices. Always identify only intersection points where perpendicular lines meet at 90-degree angles.

Practice Quiz

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Determine which lines are parallel to one another?

FAQ

Everything you need to know about this question

What exactly is a vertex in geometry?

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A vertex is a point where two or more lines intersect to form an angle. Think of it as a corner where lines meet!

Why aren't all the labeled points A through J vertices?

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Some points like A, B, I, and J are just endpoints of lines, not intersection points. Only points where lines actually cross each other count as vertices.

How can I tell which intersections create vertices?

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Look for the small square symbols in the diagram! These mark the right angles (90°) where perpendicular lines intersect, creating true vertices.

Do I need to know the angle measurements?

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No! You just need to identify where lines intersect. The square markers help you spot the perpendicular intersections, but any line intersection creates a vertex.

What if I can't see all the intersection points clearly?

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Follow each line carefully and mark where it crosses another line. Use the labels and square markers as guides to help identify the intersection points.

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