If the ratio of the legs of a right triangle is 1 : 2, then the ratio of the corresponding segments of the
hypotenuse made by a perpendicular upon it from the vertex is
To find the ratio of the corresponding segments of the hypotenuse made by a perpendicular upon it from the vertex, we can use similar triangles.
Let's assume the right triangle has legs of length 1 and 2.
The first step is to draw the right triangle and label its sides. Let's call the leg adjacent to the 1 unit side as 'a', the leg adjacent to the 2 unit side as 'b', and the hypotenuse as 'c'.
Since the ratio of the legs is given as 1:2, we can assign a value to 'a'. Let's assume 'a' is equal to 1.
Thus, 'b' will be equal to 2 (since the ratio is 1:2).
Now we need to find the ratio of the corresponding segments of the hypotenuse. Let's call the lengths of these segments 'x' and 'y'.
Using similar triangles, we can establish the following relationship:
x/y = a/b
Substituting the values, we get:
x/y = 1/2
Therefore, the ratio of the corresponding segments of the hypotenuse is 1:2.
In general, if the ratio of the legs of a right triangle is a:b, then the ratio of the corresponding segments of the hypotenuse made by a perpendicular upon it from the vertex will also be a:b.