SOLUTION: I am a 10th grade in geometry. Please help me with this proof. Given: rhombus ABCD, line DEF, line ABF, and E is the midpoint of line DF. I have to prove that line AD is congru

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Question 175013: I am a 10th grade in geometry. Please help me with this proof.
Given: rhombus ABCD, line DEF, line ABF, and E is the midpoint of line DF.
I have to prove that line AD is congruent to line BF.
I marked the diagram marking drawing line DE congruent to line EF.
From this point I dont know where to start. Please help me.
Answer by Mathtut(3670)   (Show Source): You can put this solution on YOUR website!


*************************************************************************
            statement                            reason
*************************************************************************

1. rhombus ABCD                               1. Given
   line DEF, line ABF
   E is the midpoint of line DF

2. DE congruent to EF                         2. definition of midpoint

3. DC congruent to AD                         3. def. of rhombus

4. angle CDE congruent angle BFE              4. alternate interior angles
                                                 transversal to  parallel line
                                                 ABF and DC

5. BEF congruent to DEC                       5.opposite angles of intersecting
                                                lines
                                                                                                                                                            6.tri BFE and tri CDE congruent               6. ASA

7. DC congruent BF                            7. CPCTC

8. BF congruent AD                            8. transitive prop (statements 
                                                 3,7)

ASA- angle side angle
:
CPCTC congruent parts of congruent triangles are congruent
:
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