Fundamental Concepts
12. The Meeting Point · When lines cross at one spot
All three lines always pass through the same point C.
Three or more lines are concurrent when they all pass through one shared point — the point of concurrency. Drag C — every line follows it because each one is anchored to that point.
What this lesson covers
Try to break it
Let's move this point around. Watch how the lines follow it, staying connected at the same spot.
How you build it
Draw three concurrent lines.
- Place the meeting point C near the centre.
- Place point A1 somewhere away from C.
- Draw line through A1 and C (Line tool: A1 then C).
- Place point A2 in a new direction from C.
- Draw line through A2 and C.
- Place point A3 in yet another direction.
- Draw line through A3 and C. All three lines pass through the same point — concurrent.
The proof, step by step
Prove that the three lines are concurrent.
- Identify the single point where all three lines intersect.
- Verify that each line passes through this common point.
- Since they share one intersection, the lines are concurrent.
Worked example
Three or more straight lines in the same plane are said to be concurrent if they:
Concurrent lines are defined as lines that intersect at a single common point. Parallel lines never meet, perpendicular lines meet at 90°, and triangles are formed by three segments, not necessarily concurrent lines.
- Are parallel to each other
- Pass through the same point — correct
- Form a closed triangle
- Are perpendicular to each other