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Question
Refer to the following figure:
Which line segments depict the “height” of point A from the base BE?
Given that ∠ABC = ∠ACD and ∠ADE = 90∘ and ∠ABC = ∠AEB
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Refer to the following figure:
Which line segments depict the “height” of point A from the base BE?
Given that ∠ABC = ∠ACD and ∠ADE = 90∘ and ∠ABC = ∠AEB
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Solution
Height is the shortest distance of a point from a reference level. In our case, our reference level is the horizontal level BE.
The vertical distance is AD (∠ADE = 90∘) is the smallest distance of A from BE.
To prove this, let us join any other point on BE(say, C) and A. Then we have a right triangle CAD, of which AC would become the hypotenuse and hence is the longest side.
Therefore AD is the shortest and hence is the height.
Height is the shortest distance of a point from a reference level. In our case, our reference level is the horizontal level BE.
The vertical distance is AD (∠ADE = 90∘) is the smallest distance of A from BE.
To prove this, let us join any other point on BE(say, C) and A. Then we have a right triangle CAD, of which AC would become the hypotenuse and hence is the longest side.
Therefore AD is the shortest and hence is the height.
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