Triangle Median Problem: Finding DC Length When BD = 4

Q: What exactly is a median in a triangle?

A median is a line segment that connects a vertex of the triangle to the midpoint of the opposite side. Since AD is a median, point D is exactly halfway between B and C.

Q: Why must BD equal DC?

Because D is the midpoint of side BC! By definition, a midpoint divides a line segment into two equal parts. So if BD = 4, then DC must also be 4.

Q: How is this different from an altitude or angle bisector?

A median goes to the midpoint of the opposite side, an altitude is perpendicular to the opposite side, and an angle bisector divides an angle in half. Only medians guarantee equal segments!

Q: What if the triangle is not drawn to scale?

It doesn't matter! The mathematical property of medians always holds: they create equal segments. Don't rely on visual appearance - use the definition instead.

Q: Could DC be any other value besides 4?

No! Since AD is specifically stated as a median, and BD = 4, then DC must equal 4. There's no other possibility when dealing with medians.

Triangle Medians with Equal Segment Properties

AD is the median in triangle ABC.

BD = 4

Find the length of DC.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's find the length of segment D C. Ready? Here we go.

00:11 We know that A D is a median. Remember, a median splits the side it meets in half.

00:18 Based on what we have, here is the segment length we need.

00:22 Now, substitute the value of B D to find D C.

00:27 And there you go! That's our solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

AD is the median in triangle ABC.

BD = 4

Find the length of DC.

Step-by-step solution

To solve this problem, since $AD$ is a median of triangle $ABC$ , the median divides the opposite side $BC$ into two equal segments.

Given $BD = 4$ , this means that $DC$ must also be equal to 4.

Therefore, the length of $DC$ is $4$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: A median divides the opposite side into two equal segments
Property: If BD = 4, then DC must also equal 4
Check: Verify that D is the midpoint: BD = DC = 4 ✓

Common Mistakes

Avoid these frequent errors

Thinking the median creates unequal segments
Don't assume BD and DC can have different lengths = wrong answer! A median always bisects (cuts in half) the opposite side. Always remember that medians create two equal segments on the side they intersect.

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

What exactly is a median in a triangle?

A median is a line segment that connects a vertex of the triangle to the midpoint of the opposite side. Since AD is a median, point D is exactly halfway between B and C.

Why must BD equal DC?

Because D is the midpoint of side BC! By definition, a midpoint divides a line segment into two equal parts. So if BD = 4, then DC must also be 4.

How is this different from an altitude or angle bisector?

A median goes to the midpoint of the opposite side, an altitude is perpendicular to the opposite side, and an angle bisector divides an angle in half. Only medians guarantee equal segments!

What if the triangle is not drawn to scale?

It doesn't matter! The mathematical property of medians always holds: they create equal segments. Don't rely on visual appearance - use the definition instead.

Could DC be any other value besides 4?

No! Since AD is specifically stated as a median, and BD = 4, then DC must equal 4. There's no other possibility when dealing with medians.

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