three vertices of parallelogram PQRS are shown Q(8,5) R(5,1) S(2,5)
Place statements and reasons in the table to complete the proof that shows that parallelogram PQRS is a rhombus
statements reasons
blank. pythagorean theorem
blank. blank
SR=QR. substitution
SRcongruent QR. definition of congruent . line segments
PScongruent QR. property of a parallel
blank. blank.
parallelogram QRS is a rhombus. . definition of a rhombus^
Please I need answers 😭🙏🙏
Draw a graph of coordinates of the venticles of triangle ABCand parallelogram PQRS
Statements Reasons
--------------------------------------------------------------------------------------------------------------------
1. Q(8,5), R(5,1), S(2,5) Given
2. Find the distance QR Distance formula
3. QR = √[(x2 - x1)^2 + (y2 - y1)^2] Definition of distance between two points
4. QR = √[(5 - 8)^2 + (1 - 5)^2] Substitution
5. QR = √[(-3)^2 + (-4)^2] Simplification
6. QR = √[9 + 16] Simplification
7. QR = √25 Simplification
8. QR = 5 Simplification
9. QR = SR Properties of a parallelogram
10. SR = 5 Substitution
11. QR ≅ SR Definition of congruent line segments
12. RS = -QR Properties of a parallelogram
13. RS = -5 Substitution
14. PS = QR + RS Properties of a parallelogram
15. PS = 5 + (-5) Substitution
16. PS = 0 Simplification
17. PS ≅ 0 Definition of congruent line segments
18. All sides are congruent Definition of a rhombus
19. All angles are congruent Definition of a rhombus
20. QRS is a parallelogram Definition of a parallelogram
21. QRS is a rhombus Definition of a rhombus
RS ≅ RQ
PR ⊥ QS
PS ≅ PQ