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ABCD is a trapezium in which AB is parallel to CD. The diagonals AC and BD intersects at O. If OA = 6 CM and OC = 8cm

Then find the ratio of area of triangle AOD and area of triangle COD.
This question is from triangle similarity question of class 10


Given-OA=6cm OC=8cm                                                                                    now in trnglAOD and trnglCOD,                                                                         angle AOD =angle AOC(since diagonals bisect each other)                                  OD is common                                                                                                    AO=OC(since diagonals bisect each other)                                                       ⇒ trnglAOD ≡ trnglCOD, (SAS postulate)                                                            we know that area of similar triangles is the ratio of the squares on their corresponding sides                                                                                          ⇒(area of trnglAOD÷  area of trngl COD),=OA²÷OC²                                                                                                        =6³÷8²                                                                                                              =36÷64                                                                                                            =9:16                                        
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