Triangle Median Identification: Locating the Correct Line Segment

Q: How can I tell if point D is really the midpoint of BC?

Look for visual clues in the diagram! If D appears to be exactly halfway between B and C, or if there are equal marks on segments BD and DC, then D is the midpoint.

Q: Why isn't AE a median of the triangle?

Because point E is not on any side of the triangle! A median must connect a vertex to the midpoint of the opposite side, and E doesn't lie on side BC.

Q: Can a triangle have more than one median?

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

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

A median connects a vertex to the midpoint of the opposite side. An altitude is the perpendicular line from a vertex to the opposite side. They're usually different lines!

Q: Does AC count as a median?

No! AC is simply a side of the triangle, not a median. Remember: medians go from vertices to midpoints of opposite sides, not from vertex to vertex.

Triangle Medians with Midpoint Identification

Look at the triangle ABC below.

Which of the following lines is the median of the triangle?

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Step-by-step written solution

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Understand the problem

Look at the triangle ABC below.

Which of the following lines is the median of the triangle?

Step-by-step solution

To solve this problem, we apply the definition of a median in a triangle. A median is a line segment drawn from a vertex to the midpoint of the opposite side. In the diagram of the triangle ABC:

Line $AD$ originates from vertex $A$ and is directed towards point $D$ on side $BC$ .
We need to check if $D$ is the midpoint of $BC$ .
Given that $AD$ meets the definition of a median by dividing $BC$ into two equal segments, it is indeed the median.

After evaluating the possible choices:

Choice 1: $AD$ is a line from $A$ to the midpoint of $BC$ .
Choice 2: $AE$ doesn't bisect any side.
Choice 3: $EC$ is not a median.
Choice 4: $AC$ does not connect a vertex to a midpoint of the opposite side.

Therefore, the solution to the problem is that line segment AD is the median of triangle ABC.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: Median connects vertex to midpoint of opposite side
Technique: Check if point D bisects BC into equal segments
Verification: Confirm line starts at vertex and ends at midpoint ✓

Common Mistakes

Avoid these frequent errors

Confusing medians with any line from a vertex
Don't assume every line from a vertex is a median = wrong identification! A median must specifically connect to the midpoint of the opposite side. Always verify the endpoint divides the opposite side into two equal parts.

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 can I tell if point D is really the midpoint of BC?

Look for visual clues in the diagram! If D appears to be exactly halfway between B and C, or if there are equal marks on segments BD and DC, then D is the midpoint.

Why isn't AE a median of the triangle?

Because point E is not on any side of the triangle! A median must connect a vertex to the midpoint of the opposite side, and E doesn't lie on side BC.

Can a triangle have more than one median?

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

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

A median connects a vertex to the midpoint of the opposite side. An altitude is the perpendicular line from a vertex to the opposite side. They're usually different lines!

Does AC count as a median?

No! AC is simply a side of the triangle, not a median. Remember: medians go from vertices to midpoints of opposite sides, not from vertex to vertex.

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