Given that ∠E ≅ ∠H . Are lines l and m parallel? Explain why or why not.

The correct answer is: If we are given that ∠E ≅ ∠H for the given diagram, it would be sufficient information to prove that lines l and m are parallel to each other

Hint:-
1. Parallel lines- 2 co-planar lines that are equidistant from each other are called Parallel lines. Parallel lines never intersect each other.
2. Transversal- A line that crosses 2 co-planar lines at 2 distinct points is called a transversal.
3. Alternate Exterior Angles- angles formed on the outer side of a 2 lines and on the opposite sides of the transversal are called Alternate Exterior Angles.
4. When 2 parallel lines are intersected by a transversal, Alternate Exterior Angles are equal.

Step-by-step solution:-
In the given diagram, we need to prove that-
Line l is parallel to line m.
Now, ∠E and ∠H are given, which are formed on the opposite sides of the transversal and on the outer side of the lines l & m.
Hence, ∠A and ∠B are Alternate Exterior Angles.
Now, we know that Alternate Exterior angles formed between 2 lines are equal when the 2 lines are parallel to each other.
Hence, the 2 lines l & m are parallel to each other if ∠E ≅ ∠H.
Final Answer:-
∴ If we are given that ∠E ≅ ∠H for the given diagram, it would be sufficient information to prove that lines l and m are parallel to each other.