Look at the triangle below.
Which side is the height and which side is the median?
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Look at the triangle below.
Which side is the height and which side is the median?
To solve this problem, we need to analyze the roles of line segment DC in the triangle ABC:
Step 1: Identify if DC is a height
A height (altitude) is a line segment from a vertex perpendicular to the opposite side. The image suggests that line DC is vertical, with apparent perpendicularity to BC due to the presence of D near the center of the triangle, making DC a plausible height.
Step 2: Identify if DC is the median
A median divides the opposite side into two equal lengths, from a vertex. Without explicit symmetry in the image, but assuming graphic accuracy and typical diagram problems, DC can be a median if D is the midpoint.
Step 3: Confirm if DC is both a height and a median
In instances such as isosceles or equilateral triangles, a segment can be both. Given D’s position and symmetric considerations from vertex A, it's likely DC is both here.
Thus, line segment DC is both the median and the height.
Therefore, the correct answer is DC = median and height.
DC = median and height
Is DE side in one of the triangles?
Look for the small square symbol at point D in the diagram! This indicates a 90° angle, meaning DC is perpendicular to AC and therefore a height.
If point D is the midpoint of side AC, then BD is a median. In this case, since the triangle appears to be a right triangle with special properties, DC can serve as both median and height.
Yes! In isosceles triangles and right triangles with special configurations, the same line can be both. This happens when the perpendicular from a vertex also hits the midpoint of the opposite side.
In this specific right triangle configuration, segment DC satisfies both conditions: it's perpendicular to the base (making it a height) and it connects to the midpoint (making it a median).
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