Question

Pqrs is a rhombus. Diagonals pr and qs intersect at o. Prove that all 4 triangles so formed are congruent. With proper and step by step .

Answer 1

Answer:

Step by step:

letABCDis a rhombus whose all side are equal and AC⊥BD

∠AOB=∠AOD=∠COD=∠COB=90  

 

InΔABCandΔCBO

⇒AB=BC

⇒AO=CO

⇒∠BOA=∠BOC=90    

by SAS criteria ΔABO is congurent to ΔCBO

Simillary Inrighttriangle AOD and COD

⇒AD=DC

⇒∠AOD=∠COD=90  

 

⇒∴AO=AD

∴ΔAOD is congruent to ΔCOD

Hence,allfourtriangles are congruent.

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