The above proof is also helpful to prove another important theorem called the mid-point theorem. (Area of ADE)/(Area of CDE) = (1/2 × AE × DP)/(1/2 × CE × DP)īoth the triangles BDE and CDE are between the same set of parallel lines.Īrea of triangle BDE = Area of triangle CDEĪpplying this we have, (Area of triangle ADE)/(Area of triangle BDE) = (Area of triangle ADE)/(Area of triangle CDE) Both these triangles are on the same base AC and have equal height DP. Both these triangles are on the same base AB and have equal height EQ. ![]() Draw perpendicular DP perpendicular to AE and EQ perpendicular to AD.Ĭonsider the triangles ADE and BDE. In this triangle, we draw a line DE parallel to the side BC of ΔABC and intersecting the sides AB and AC at D and E, respectively.Ĭonstruction: In the above diagram, create imaginary lines where you can Join C to D and B to E. Given: Consider a triangle ΔABC, as shown in the given figure. Statement: The line drawn parallel to one side of a triangle and cutting the other two sides divides the other two sides in equal proportion. Let us now try to prove the basic proportionality(BPT) theorem statement. Proof of the Basic Proportionality Theorem Statement of Basic Proportionality TheoremĬonverse of Basic Proportionality Theorem The theorem thus also helps us better understand the concept of similar triangles. Now let us try and understand the Basic Proportionality Theorem. ![]() ![]() Corresponding sides of both the triangles are in proportion to each other.Corresponding angles of both the triangles are equal.The concept of Thales theorem has been introduced in similar triangles. If the given two triangles are similar to each other then, It gives the relationship between the sides of any two equiangular triangles. Based on this concept, the basic proportionality theorem(BPT) was proposed. Basic proportionality theorem was proposed by a famous Greek mathematician, Thales, hence, it is also referred to as the Thales theorem. According to the famous mathematician, for any two equiangular triangles, the ratio of any two corresponding sides of the given triangles is always the same.
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