Finding the Median in Triangle ABC: Geometric Construction Problem

Triangle Medians with Midpoint Identification

What is the median of triangle ABC?

AAABBBDDDCCCEEEFFF

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Step-by-step written solution

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1

Understand the problem

What is the median of triangle ABC?

AAABBBDDDCCCEEEFFF

2

Step-by-step solution

To determine the median of triangle ABC, we must identify a segment connecting a vertex of the triangle to the midpoint of the opposite side.

Examining the diagram, point F appears to be located on side AC. Given the configuration, point F divides side AC into two equal segments, which makes F the midpoint of AC.

Therefore, segment CF connects vertex C to the midpoint F of side AC. This characteristic aligns with the definition of a median in a triangle.

Hence, the median of triangle ABC is CF CF .

3

Final Answer

CF

Key Points to Remember

Essential concepts to master this topic
  • Definition: A median connects a vertex to the midpoint of the opposite side
  • Technique: Identify the midpoint by equal segment markings or visual symmetry
  • Check: Verify the segment goes from vertex to midpoint of opposite side ✓

Common Mistakes

Avoid these frequent errors
  • Confusing medians with altitudes or angle bisectors
    Don't identify any line from a vertex as a median = wrong geometric element! Altitudes are perpendicular to sides, angle bisectors split angles equally. Always confirm the line connects a vertex to the midpoint of the opposite side.

Practice Quiz

Test your knowledge with interactive questions

Is DE side in one of the triangles?
AAABBBCCCDDDEEE

FAQ

Everything you need to know about this question

How do I identify the midpoint on a triangle diagram?

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Look for equal segment markings (like small perpendicular lines) or visual symmetry. In this diagram, point F appears to divide side AC into two equal parts, making it the midpoint.

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

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A median connects a vertex to the midpoint of the opposite side, while an altitude is perpendicular to the opposite side. Medians focus on midpoints, altitudes focus on right angles.

Can a triangle have more than one median?

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

Why is CF the correct answer and not CE?

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CF connects vertex C to point F (the midpoint of side AC), which matches the median definition. CE connects vertex C to point E, but E is not the midpoint of any side of triangle ABC.

How can I remember what a median is?

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Think "middle" - a median goes to the middle point (midpoint) of the opposite side. The word "median" contains "med" which relates to "middle"!

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