The ratio of corresponding sides of two similar triangles are in the ratio 3:5 then the ratio between their medians is
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The ratio of corresponding sides of two similar triangles are in the ratio 3:5 then the ratio between their medians is
answer it with explanation
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To determine the ratio between the medians of two similar triangles let's first understand what medians are in a triangle.
A median of a triangle is a line segment drawn from one vertex of the triangle to the midpoint of the opposite side. Essentially it connects a vertex to the midpoint of the opposing side.
In a triangle each side has a corresponding median. The medians divide each other in a ratio of 2:1. That is a median divides the opposite side into two segments with the segment closer to the vertex being twice as long as the segment closer to the midpoint.
Now let's consider two similar triangles. Similar triangles have corresponding angles that are equal and their corresponding sides are proportional.
Given that the corresponding sides of the two similar triangles are in the ratio 3:5 we can assume that the longer side of the first triangle corresponds to the longer side of the second triangle.
Let the lengths of the corresponding sides of the triangles be 3x and 5x respectively where x is a constant.
Since the medians of the triangles divide the sides into segments with a ratio of 2:1 the lengths of the medians will be 2x and 3x for the first triangle and 4x and 6x for the second triangle.
To find the ratio between the medians we divide the lengths of the corresponding medians:
(2x/4x) : (3x/6x) = 1/2 : 1/2 = 1:1
Therefore the ratio between the medians of the two similar triangles is 1:1.