Question

Ray knows that the m∠3 = m∠6. Which of the following conclusions can Ray make based on the given information?

Lines l and m are parallel because alternate interior angles are equal.
Lines l and m are parallel because alternate exterior angles are equal.
Lines l and m are parallel because corresponding angles are equal.
No conclusion can be made about the lines.

Answer 1

Its A.

Explanation:

Answer 2

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.