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 height of a triangle is defined as the perpendicular distance from a vertex to the line containing the opposite side (base). In this problem, we observe a vertical line segment drawn from a point on the base (horizontal line at the bottom of the triangle) to some level above the base. To determine if this line is a height, it must be perpendicular to the base and also reach to the opposite vertex of the triangle.
In the provided figure, the vertical line extends vertically from the base but does not connect to the opposite vertex of the triangle (at the top). Instead, it terminates at some intermediate point above the base. Since the line does not satisfy the full condition of being perpendicular and reaching an opposite vertex, it cannot be considered the height of this triangle.
Therefore, the given straight line is not the height of the triangle.
The correct and final answer is: No.
No
Is the straight line in the figure the height of the triangle?
A triangle's height (altitude) must satisfy two conditions: it must be perpendicular to one side of the triangle AND it must connect that side to the opposite vertex. Missing either condition means it's not a height.
Yes! Every triangle has three heights - one from each vertex to the opposite side. Each height is perpendicular to its corresponding base and reaches the opposite vertex.
Then it's not a height of the triangle! It might be perpendicular to the base, but without connecting to the opposite vertex, it's just a perpendicular line segment, not an altitude.
Not always! In obtuse triangles, some heights fall outside the triangle. The important thing is that the height line (extended if needed) is perpendicular to the base and passes through the opposite vertex.
Look carefully at where the line ends. The height must start from one side (base) and end exactly at the corner point (vertex) opposite to that side. If it stops anywhere else, it's not a height.
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