Is the straight line in the figure the height of the triangle?
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Is the straight line in the figure the height of the triangle?
The triangle's altitude is a line drawn from a vertex perpendicular to the opposite side. The vertical line in the diagram extends from the triangle's top vertex straight down to its base. By definition of altitude, this line is the height if it forms a right angle with the base.
To solve this problem, we'll verify that the line in question satisfies the altitude condition:
Therefore, the straight line depicted is indeed the height of the triangle. The answer is Yes.
Yes
Is the straight line in the figure the height of the triangle?
An altitude must meet two conditions: it starts from a vertex AND is perpendicular to the opposite side. Just connecting a vertex to the opposite side isn't enough!
Look for right angle symbols (small squares) or check if the line is vertical when the base is horizontal. In this diagram, the vertical line to the horizontal base shows perpendicularity.
Yes! Every triangle has exactly three altitudes - one from each vertex to its opposite side. They don't all have to be inside the triangle either.
An altitude is perpendicular to the opposite side, while a median connects a vertex to the midpoint of the opposite side. They're usually different lines!
Not always! In obtuse triangles, some altitudes fall outside the triangle. But in this acute triangle, the altitude from the top vertex stays inside.
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