Which side of triangle ABC is both the median and the height drawn to?
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Which side of triangle ABC is both the median and the height drawn to?
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:
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
Is the straight line in the figure the height of the triangle?
A median connects a vertex to the midpoint of the opposite side. A height is perpendicular from a vertex to the opposite side. In isosceles triangles, these can be the same line!
Look for visual symmetry - if the triangle appears to have two equal sides or a vertical line of symmetry, it's likely isosceles. The perpendicular from the vertex angle will bisect the base.
In an isosceles triangle, the vertex angle sits directly above the midpoint of the base. So the line from vertex to midpoint is automatically perpendicular, making it both median and height!
In a general triangle, the median and height from any vertex are different lines. They only coincide in isosceles triangles when drawn from the vertex angle to the base.
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