Triangle ABC Median: Identify the Connecting Line and Its Base Side

Q: How can I tell if point E is really the midpoint of AC?

Point E is the midpoint if it divides AC into two equal segments: AE = EC. In diagrams, midpoints are often marked with tick marks or clearly labeled.

Q: Why is BE the median and not BD?

BD connects vertex B to point D, but D is not on the opposite side AC - it appears to be outside the triangle. A median must connect to the opposite side, and E is on side AC.

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 the perpendicular line from a vertex to the opposite side (or its extension).

Q: Does the median always stay inside the triangle?

In acute and right triangles, yes! But in obtuse triangles, some altitudes can fall outside. However, medians always connect vertex to midpoint, so they stay within the triangle's boundaries.

Triangle Medians with Midpoint Identification

Look at triangle ABC below.

What is the median of the triangle and to which side is it drawn?

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at triangle ABC below.

What is the median of the triangle and to which side is it drawn?

Step-by-step solution

A median of a triangle is a line segment that connects a vertex to the midpoint of the opposite side. In triangle $\triangle ABC$ , we need to identify such a median from the diagram provided.

Step 1: Observe the diagram to identify the midpoint of each side.

Step 2: It is given that point $E$ is located on side $AC$ . If $E$ is the midpoint of $AC$ , then any line from a vertex to point $E$ would be a median.

Step 3: Check line segment $BE$ . This line runs from vertex $B$ to point $E$ .

Step 4: Since $E$ is labeled as the midpoint of $AC$ , line $BE$ is the median of $\triangle ABC$ drawn to side $AC$ .

Therefore, the median of the triangle is $BE$ for $AC$ .

Final Answer

BE for AC

Key Points to Remember

Essential concepts to master this topic

Definition: A median connects vertex to opposite side's midpoint
Technique: Find midpoint E on AC, then draw line BE
Check: Verify E divides AC into two equal segments ✓

Common Mistakes

Avoid these frequent errors

Confusing median with any line from vertex
Don't draw BE just because it connects vertex B to side AC = wrong median! The line must connect to the exact midpoint, not any random point on the opposite side. Always verify the point divides the 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 E is really the midpoint of AC?

Point E is the midpoint if it divides AC into two equal segments: AE = EC. In diagrams, midpoints are often marked with tick marks or clearly labeled.

Why is BE the median and not BD?

BD connects vertex B to point D, but D is not on the opposite side AC - it appears to be outside the triangle. A median must connect to the opposite side, and E is on side AC.

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 the perpendicular line from a vertex to the opposite side (or its extension).

Does the median always stay inside the triangle?

In acute and right triangles, yes! But in obtuse triangles, some altitudes can fall outside. However, medians always connect vertex to midpoint, so they stay within the triangle's boundaries.

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