Given: ∠3 = ∠6, Two lines l and m.
To Find: Conclusions based on given information
Construction: Drawn two lines l and m (1.) when l and m are parallel (2) when l and m are not parallel.
Solution:
1. Lines l and m are parallel because alternate interior angles are equal.[ False, not given whether ∠3 and ∠6,are which angles.]
2. Lines l and m are parallel because alternate exterior angles are equal.[ False, not given whether ∠3 and ∠6,are which angles.]
3. Lines l and m are parallel because corresponding angles are equal. [False, not given whether ∠3 and ∠6,are which angles.]
4.No conclusion can be made about the lines.→ [ True]
If the lines are intersecting then also two angles can be equal .
If lines are parallel, then ∠3 and∠6 can be vertically opposite angles also.
