Triangle Median Identification: Locating the Correct Line Segment in ABC

Q: How can I tell if a point is really the midpoint?

A midpoint divides a side into two equal parts. In the diagram, point E appears to be equidistant from A and C, making $ AE = EC $.

Q: Why isn't AD a median if it comes from vertex A?

While AD starts from vertex A, point D is not the midpoint of side BC. A median must connect to the exact midpoint of the opposite side.

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: 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 perpendicular from a vertex to the opposite side (not necessarily the midpoint).

Q: How do I identify the midpoint in a diagram?

Look for visual cues like equal tick marks, equal measurements, or points that appear to divide a side into two equal segments. The midpoint is exactly halfway along the side.

Triangle Medians with Midpoint Recognition

The triangle ABC is shown below.

Which line segment is the median?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Identify the median of the following triangle

00:04 BE bisects AC according to the given data

00:09 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The triangle ABC is shown below.

Which line segment is the median?

Step-by-step solution

To solve this problem, we need to identify the median in triangle ABC:

Step 1: Recall the definition of a median. A median is a line segment drawn from a vertex to the midpoint of the opposite side.
Step 2: Begin by evaluating each line segment based on the definition.
Step 3: Identify points on triangle ABC:

AD is from A to a point on BC.
BE is from B to a point on AC.
FC is from F to a point on AB.

Step 4: Determine if these points (D, E, F) are midpoints:

Since BE connects B to E, and E is indicated to be the midpoint of segment AC (as shown), BE is the median.
AD and FC, by visual inspection, do not connect to midpoints on BC or AB respectively.

Therefore, the line segment that represents the median is $BE$ .

Thus, the correct answer is: BE

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: A median connects a vertex to the midpoint of opposite side
Identification: Look for line segment BE connecting vertex B to midpoint E on AC
Verification: Check that E divides AC into two equal segments AE = EC ✓

Common Mistakes

Avoid these frequent errors

Confusing any line segment from a vertex as a median
Don't assume AD or FC are medians just because they start from vertices = wrong identification! These don't connect to midpoints of opposite sides. Always verify the endpoint is exactly 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 can I tell if a point is really the midpoint?

A midpoint divides a side into two equal parts. In the diagram, point E appears to be equidistant from A and C, making $AE = EC$ .

Why isn't AD a median if it comes from vertex A?

While AD starts from vertex A, point D is not the midpoint of side BC. A median must connect to the exact midpoint of the opposite side.

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.

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 perpendicular from a vertex to the opposite side (not necessarily the midpoint).

How do I identify the midpoint in a diagram?

Look for visual cues like equal tick marks, equal measurements, or points that appear to divide a side into two equal segments. The midpoint is exactly halfway along the side.

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