Given |AB| cong to |CD|, |AD| cong to |BC|, prove |AB| par to |CD|, |AD| par to |BC

[Tmdan4357]

Hello I need some help on this problem

 

[Deleted member 4993]

Hello I need some help on this problem

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[stapel]

Hello I need some help on this problem

diagram:
      A*-----------*B
      /1\4        /
     /   \       /
    /     \     /
   /       \   /
  /        2\3/
D*-----------*C

\(\displaystyle \mbox{Given: }\, \overline{AB}\, \cong\, \overline{CD};\, \overline{AD}\, \cong\, \overline{BC}\)

\(\displaystyle \mbox{Prove: }\, \overline{AB}\, \|\, \overline{CD};\, \overline{AD}\, \|\, \overline{BC}\)

Hint: If one extends AB, DC, and AC, what can one say about angles 4 and 2? What about extending AD, BC, and AC, with respect to angles 1 and 3? What then about triangles ADC and ABC?