Determine whether the statement is true or false.
AD is the height in the triangle ABC.
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Determine whether the statement is true or false.
AD is the height in the triangle ABC.
To determine if AD is the height of triangle ABC, we start by recalling the definition of a height in a triangle. A height is a perpendicular line segment from a vertex to the line containing the opposite side. In triangle geometry, for AD to be considered a height, it must be perpendicular to the line BC.
The given diagram shows that AD is indeed perpendicular to BC, as denoted by the perpendicular symbol (the small square at the intersection indicating a angle). This matches the definition of a height in a triangle, which is a line drawn perpendicular from a vertex (in this case, vertex A) to the line containing the opposite side (here, BC).
Since AD meets this criterion of being perpendicular to the opposite side, we can conclusively state that AD is indeed the height of the triangle ABC. Thus, the statement "AD is the height in the triangle ABC" is true.
Therefore, the solution to the problem is True.
True.
Is DE side in one of the triangles?
Look for the right angle symbol (small square) where the lines meet. In diagrams, this symbol specifically indicates a angle, confirming perpendicularity.
Yes! Every triangle has three heights - one from each vertex to the opposite side. Each height creates a right angle with its corresponding base.
They're the same thing! Height and altitude both refer to the perpendicular distance from a vertex to the opposite side. Both terms are used interchangeably in geometry.
Not always! In acute triangles, all heights are inside. But in obtuse triangles, some heights fall outside the triangle and meet the extended opposite side.
The height represents the shortest distance from a vertex to the opposite side. Only a perpendicular line gives this minimum distance - any other line would be longer!
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