Triangle Construction: Identifying Median and Altitude Locations

Triangle Analysis with Missing Construction Elements

The triangle ABC is shown below.

To which side are the median and the altitude drawn?

AAABBBCCCDDDEEE

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine which side the median and the height are drawn to in the following triangle
00:03 CE bisects AB according to the given information
00:12 AD is perpendicular to DB (forms a right angle with it)
00:17 It would seem that the perpendicular and the median are drawn to different sides
00:20 This is the solution to the question

Step-by-step written solution

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1

Understand the problem

The triangle ABC is shown below.

To which side are the median and the altitude drawn?

AAABBBCCCDDDEEE

2

Step-by-step solution

In the problem of determining which side of triangle ABC has a median and an altitude drawn, we begin by understanding the role of these geometric features:

Medians: A median originates from one vertex and connects to the midpoint of the opposing side. Therefore, it must appear as a line bisecting opposite side.

Altitudes: An altitude also starts from a vertex but descends perpendicularly to the opposite side, forming a right angle.

In exploring the labels and positional intersection lines on the provided diagram, if available, we do not find a clear depiction through the labels and positions alone, which allows us to exactly pinpoint a side being bisected or with a right angle from a vertex. The problem declaratively assures no qualification dominantly demonstrating altitude (notably not perpendicular) or median (not clearly bisecting any side).

Thus, the correct choice and conclusion is that neither is correctly shown in respecting any side of the triangle ABC.

Therefore, no side of triangle ABC has a defined median and altitude drawn distinctly according to known geometric properties and referential diagram analysis.

No side

3

Final Answer

No side

Key Points to Remember

Essential concepts to master this topic
  • Median Definition: Line from vertex to midpoint of opposite side
  • Altitude Definition: Perpendicular line from vertex to opposite side forming 90°
  • Visual Analysis: Check diagram for right angle marks and midpoint indicators ✓

Common Mistakes

Avoid these frequent errors
  • Assuming any line segment is a median or altitude
    Don't assume every line from vertex to side is a median or altitude = wrong identification! Lines must meet specific criteria: medians bisect sides exactly, altitudes form 90° angles. Always verify that construction marks show perpendicularity or midpoint division.

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 line is a median from the diagram?

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Look for tick marks that show the line divides the opposite side into two equal parts. A median connects a vertex to the exact midpoint of the opposite side.

What visual clues show an altitude in a triangle?

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An altitude is marked with a small square symbol (⊥) where the line meets the opposite side, indicating a 90-degree angle. Without this mark, it's not an altitude!

Can a line be both a median and an altitude?

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Yes! In isosceles triangles, the line from the vertex angle to the base is both a median and altitude. In equilateral triangles, all three medians are also altitudes.

What if I don't see any special markings on the diagram?

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If there are no perpendicular marks or midpoint indicators, then the lines shown are likely just regular line segments, not medians or altitudes. Always look for the specific geometric symbols!

Why does this triangle show 'No side' as the answer?

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The diagram doesn't show proper construction markings for either medians or altitudes. Without right angle symbols or midpoint marks, we cannot identify any side as having these special line segments drawn to it.

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