congruence of triangles


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Proof:
In triangles AOB and COD, AO = CO (given) BO = OD (given) (vertically opposite angles are equal) D AOB D COD (SAS congruency condition) Since these are alternate angles made by the transversal AC intersecting AB and CD. AB||CD Similarly, AD||BC Hence ABCD is a parallelogra..
Proof:
A rhombus is a parallelogram such that AB=DC=AD=BC ---(i) Also the diagonals of a parallelogram bisect each other. Hence BO=DO and AO=OC ---(ii) Now compare triangles AOB and AOD, AB=AD (from (i) above) BO=DO (from (ii) above) AO=AO (common side) (SSS congruency condition) (corr..
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