SOLUTION: Hi! How Are You?! im having trouble with this proof can u please help me?! Rhombus ABCD Given Line AB is parallel to line CD Line AB is congruent to line CD Lin

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Question 173906: Hi! How Are You?! im having trouble with this proof can u please help me?!
Rhombus ABCD
Given
Line AB is parallel to line CD
Line AB is congruent to line CD
Line AC is perpendicular to BD
Prove:
ABCD is a Rhombus
i dont get it so please help me thank you..
Answer by Mathtut(3670)   (Show Source): You can put this solution on YOUR website!


 


.............................................................................

             Statement                             Reason

1. AB is parallel CD                     1. Given
   AB is congruent to CD
   AC is perpendicular to BD

2. angle CDB congruent to angle ABD      2. BD transversal-Alt interior
                                            angles.

3. BD congruent BD                       3. reflexive prop

4. tri BCD is congruent to tri BAD       4. SAS  

5. AD congruent BC                       5. CPCTC

6. angle ABD congruent angle CBD         6. CPCTC
   angle CDB congruent angle BDA

7. angle CBD congruent angle BDA         7. transitive prop  S #2,6

8. BC is parallel to AD                  8. alternate interior angles converse

9. ABCD is a paralleogram                9. def of parallelogram S #1,8

10.ABCD is a Rhombus                     10 def of a rhombus  S #1,5,9

SAS side angle side theorem
CPCTC- corresponding parts of congruent triangles are congruent
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