Triangle Median Identification: Line Segment Analysis in ABC Triangle

Q: How do I know if F is really the midpoint of AB?

Look for visual clues in the diagram! The problem shows F positioned exactly halfway between A and B. You can also check if the diagram indicates equal segments $ AF = FB $.

Q: What's the difference between a median and an altitude?

A median goes from a vertex to the midpoint of the opposite side. An altitude goes from a vertex perpendicular to the opposite side (making a 90° angle).

Q: Can a triangle have more than one median?

Yes! Every triangle has exactly three medians - one from each vertex to the midpoint of the opposite side. They all meet at a special point called the centroid.

Q: Could DE + FC be a median?

No! A median is a single line segment, not the sum of two segments. Adding segments together doesn't create a median - you need one continuous line from vertex to midpoint.

Triangle Medians with Midpoint Recognition

Look at the triangle ABC below.

Which of the line segments is the median?

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the triangle ABC below.

Which of the line segments is the median?

Step-by-step solution

To identify the median in triangle $ABC$ , we will utilize the definition of a median: it is the line segment extending from a vertex of the triangle to the midpoint of the opposite side.

In the diagram, triangle $ABC$ is formed with vertices $A$ , $B$ , and $C$ . We need to identify which of the segments is drawn from a vertex and intersects the opposite side at its midpoint.

Examine segment $FC$ :

$F$ appears to be a midpoint of side $AB$ of the triangle $ABC$ .
Line segment $FC$ originates from vertex $C$ and extends to $F$ .

The segment $FC$ meets the criteria for a median as it connects vertex $C$ to the midpoint of $AB$ .

Therefore, we conclude that the median of triangle $ABC$ is FC.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: A median connects a vertex to the midpoint of the opposite side
Identification: Look for segments from vertex C to midpoint F on side AB
Verification: Check that F divides AB into two equal parts visually ✓

Common Mistakes

Avoid these frequent errors

Confusing any line segment with a median
Don't assume every line segment in a triangle is a median = wrong identification! Many segments like altitudes, angle bisectors, or random lines aren't medians. Always verify the segment starts at a vertex and ends at the midpoint of the opposite side.

Practice Quiz

Test your knowledge with interactive questions

Is the straight line in the figure the height of the triangle?

FAQ

Everything you need to know about this question

How do I know if F is really the midpoint of AB?

Look for visual clues in the diagram! The problem shows F positioned exactly halfway between A and B. You can also check if the diagram indicates equal segments $AF = FB$ .

What's the difference between a median and an altitude?

A median goes from a vertex to the midpoint of the opposite side. An altitude goes from a vertex perpendicular to the opposite side (making a 90° angle).

Can a triangle have more than one median?

Yes! Every triangle has exactly three medians - one from each vertex to the midpoint of the opposite side. They all meet at a special point called the centroid.

Why isn't HG a median?

HG doesn't start at a vertex of triangle ABC. Point H appears to be on side AC, not at vertex A, B, or C. Medians must originate from vertices.

Could DE + FC be a median?

No! A median is a single line segment, not the sum of two segments. Adding segments together doesn't create a median - you need one continuous line from vertex to midpoint.

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