Triangle Median Verification: Is AD a True Median in Triangle ABC?

Question

Determine whether the statement is true or false.

AD is the median in the triangle ABC.

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Video Solution

Solution Steps

00:00 Determine whether AD is the median in the triangle
00:03 AD is the altitude according to the given information ( it forms a right angle with the side)
00:07 If the triangle were an isosceles triangle, then the height would also be the median
00:17 However we don't know if the triangle is an isosceles triangle
00:20 Therefore we don't know if the altitude is also a median
00:23 This is the solution

Step-by-Step Solution

To determine if AD is the median of triangle ABC, we recall that a median connects a vertex to the midpoint of the opposite side. In this scenario, we would need to verify if point D is indeed the midpoint of side BC.

As a median divides the opposite side into two equal halves, our task would be to confirm the equality of segments BD and DC with available information or measurements.

However, the problem does not provide specific measurements, coordinates, or other information necessary to confirm that D is the midpoint of BC. Without this critical information, it is impossible to ascertain whether AD is a median.

Therefore, the conclusion is that the statement about AD being a median cannot be determined with the given data.

Thus, the correct answer to the problem is: Impossible to determine.

Answer

Impossible to determine.