contestada

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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.
Response area means blank
The answers are Congruent segments, a rhombus, a parallelogram, SSS congruence postulate, ASA congruence postulate, SAS congruence postulate, CPCTC, they are adjacent, and vertical angles are congruent

Respuesta :

The completed proof is presented as follows;

By definition of a rhombus [tex]\overline{JK} \cong \overline{KM}[/tex] and by the reflexive property of

congruence [tex]\overline{KP} \cong \overline{KP}[/tex], because the diagonals of a rhombus bisect a pair

of opposite angles, ∠JKP ≅ ∠MKP, making ΔJKP ≅ ΔMKP by the SAS

congruency postulate, because CPCTC, ∠JPK ≅ ∠MPK, and these angles

are right angles because two angles that form a linear pair are congruent,

thereby making, [tex]\overline{JK} \perp \overline{KM}[/tex] by definition of perpendicular segments.

Reasons:

Please find attached the drawing of the given rhombus JKMH, that show

the point of intersection of the diagonals JM and HK at point P.

  • A rhombus is an equilateral quadrilateral, therefore, the adjacent sides [tex]\overline{JK} \ and \ \overline{KM}[/tex] are congruent.

  • The SAS congruency postulate states that if a triangle has two sides and an included angle that are congruent to two sides and an included angle of another triangle, then the two triangles are congruent.

  • CPCTC is an acronym for Congruent Parts of Congruent Triangles are Congruent.

Learn more about the properties of a rhombus here:

https://brainly.com/question/10618409

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