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25.01.2021 •
Mathematics
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Given: Rhombus JKMH with diagonals intersecting at point P
Rhombus J K M H with diagonals J M and H K intersecting at P
Prove: JM⎯⎯⎯⎯⎯⊥HK⎯⎯⎯⎯⎯⎯
By the definition of Response area, JK⎯⎯⎯⎯⎯≅KM⎯⎯⎯⎯⎯⎯ and by the reflexive property of congruence, KP⎯⎯⎯⎯⎯≅KP⎯⎯⎯⎯⎯ . Because the diagonals of a rhombus bisect a pair of opposite angles, ∠JKP≅∠MKP , making △JKP≅△MKP by the Response area. Because Response area, ∠JPK≅∠MPK, and these angles are right angles because two angles that form a linear pair are congruent, thereby making JM⎯⎯⎯⎯⎯⊥HK⎯⎯⎯⎯⎯⎯ by the definition of perpendicular segments.
congruent segmentsa rhombusa parallelogramSSS congruence postulateASA congruence postulateSAS congruence postulateCPCTCthey are adjacentvertical angles are congruent
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