The complete proof from the figure is:
- AC ≅ DF; AB ≅ DE; ∠1 ≅ ∠6 -- Given
- ∠1 ≅ ∠2; ∠5 ≅ ∠6 -- vertical angles
- ∠2 ≅ ∠5 --- corresponding angles
- ΔABC ≅ ΔDEF --- SAS postulate
- ∠3 ≅ ∠4 --- corresponding angles
- BC || EF ---- proved
How to complete the proof?
The given parameter is:
AC ≅ DF; AB ≅ DE; ∠1 ≅ ∠6
Angles 1 and 2, & Angles 5 and 6 are vertical angles
So, we have: ∠1 ≅ ∠2; ∠5 ≅ ∠6 by the definition of vertical angles.
From the figure, triangles ABC and DEF are congruent by the SAS postulate.
So, we have: ΔABC ≅ ΔDEF by the definition of SAS postulate
Angles 3 and 4 are corresponding angles
So, we have: ∠1 ≅ ∠2; ∠5 ≅ ∠6 by the definition of corresponding angles.
Hence, the lines BC and EF are parallel lines
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