Triangle ABC: Identifying the Side with Coinciding Median and Height

Which side of triangle ABC is both the median and the height drawn to?

CCCAAABBBDDDEEEFFF

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Step-by-step video solution

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00:00 Determine which side the median and the height are drawn to in the following triangle
00:03 CE bisects AB
00:10 AC is perpendicular to AB (forming a right angle)
00:18 This is the solution to the question

Step-by-step written solution

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1

Understand the problem

Which side of triangle ABC is both the median and the height drawn to?

CCCAAABBBDDDEEEFFF

2

Step-by-step solution

To solve this problem, we need to use the properties of medians and heights, specifically in isosceles triangles. In an isosceles triangle, the median from the vertex angle to the base is also the height. In the diagram of triangle ABC, given the problem context and a typical configuration of an isosceles triangle, we can see that:

  • The side AB is horizontally aligned in the diagram.
  • The point D, directly below A, suggests that the median from A also serves as the height to the base BC, if AB = BC making triangle ABC isosceles.

Therefore, in triangle ABC, side AB is both the median and the height of the triangle, assuming a vertical symmetry along median AD, characteristic of an isosceles triangle configuration.

Therefore, the correct answer is AB AB .

3

Final Answer

AB

Practice Quiz

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Fill in the blanks:

In an isosceles triangle, the angle between two ___ is called the "___ angle".

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