Triangle Median and Altitude: Identifying Lines in Triangle ABC

Triangle Properties with Median and Altitude Identification

The triangle ABC is shown below.

To which side(s) are the median and the altitude drawn?

AAABBBCCCDDDEEEFFF

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Step-by-step written solution

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1

Understand the problem

The triangle ABC is shown below.

To which side(s) are the median and the altitude drawn?

AAABBBCCCDDDEEEFFF

2

Step-by-step solution

To solve the problem of identifying to which side of triangle ABC ABC the median and the altitude are drawn, let's analyze the diagram given for triangle ABC ABC .

  • We acknowledge that a median is a line segment drawn from a vertex to the midpoint of the opposite side. An altitude is a line segment drawn from a vertex perpendicular to the opposite side.
  • Upon reviewing the diagram of triangle ABC ABC , line segment AD AD is a reference term. It appears to meet point C C in the middle, suggesting it's a median, but it also forms right angles suggesting it is an altitude.
  • Given the placement and orientation of AD AD , it is perpendicular to line BC BC (the opposite base for the median from A A ). Therefore, this line is both the median and the altitude to side BC BC .

Thus, the side to which both the median and the altitude are drawn is BC.

Therefore, the correct answer to the problem is the side BC BC , corresponding with choice Option 2: BC \text{Option 2: BC} .

3

Final Answer

BC

Key Points to Remember

Essential concepts to master this topic
  • Definition: Median connects vertex to midpoint of opposite side
  • Technique: Altitude forms right angle with perpendicular symbol in diagram
  • Check: Both lines from vertex A go to side BC ✓

Common Mistakes

Avoid these frequent errors
  • Confusing which side the line is drawn TO versus drawn FROM
    Don't identify the vertex where the line starts = wrong answer! Students often name the side adjacent to the vertex instead of the opposite side. Always identify which side the median/altitude meets or is perpendicular to.

Practice Quiz

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Is the straight line in the figure the height of the triangle?

FAQ

Everything you need to know about this question

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. An altitude is perpendicular to the opposite side (shown with a right angle symbol). Sometimes they can be the same line!

How do I know which side the line is drawn to?

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Look at where the line ends, not where it starts! The line goes from vertex A to side BC, so it's drawn to side BC.

Can a line be both a median and altitude at the same time?

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Yes! In some triangles, especially isosceles triangles, the median and altitude from a vertex to the opposite side can be the same line segment.

What if the altitude doesn't look perpendicular in the diagram?

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Look for the right angle symbol (small square) near where the line meets the side. This symbol tells you it's perpendicular, even if the drawing isn't perfectly to scale.

Why are there multiple lines in this triangle diagram?

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The diagram shows different medians and altitudes from various vertices. Focus on identifying which lines go to which sides - that's what the question is asking!

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