Results On Ratio of the Areas of Two Similar Triangles
Theorem 1: The ratio of the areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides.
Theorem 2: The areas of two similar triangles are in the ratio of the squares of the corresponding altitudes.
Theorem 3: The areas of two similar triangles are in the ratio of the squares of the corresponding medians.
Theorem 4: The areas of two similar triangles are in the ratio of the squares of corresponding angle bisector segments.
Theorem 5: If the areas of two similar triangles are equal, then the triangles are congruent i.e., equal and similar triangles are congruent. Two figures are similar if one of them is exact scale model of the other.
(E) The line segment joining the midpoint of any two sides of a triangle, is parallel to the third side and equal to half of it.
The line drawn through the mid-point of one triangle, parallel to another side, intersects the third side at its mid-point.
If there are three parallel lines and the intercepts made by them on one transversal are equal, then the intercepts on any other transversal are also equal.
Here, AB = BC = DE = EF.
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