determine if l || m based on the information given on the diagram. If yes, state the converse that proves the lines are parallel.

The converse which would serve as prove that l is parallel to m are given in the answers below:

Considering the information in the given diagrams:

1. Yes, l is parallel to m.

The converse is: "If corresponding angles are equal, then  l is parallel to m".  One of the corresponding angles plus equals .

Thus, l || m.

2. Yes, l is parallel to m.

The converse is: "if two angles are linear pair, then they sum up to ".

So then, l || m.

3. Yes, l is parallel to m.

The converse is: "if two corresponding angles are right angles, then they are congruent".

Therefore, l || m.

4. Yes, l is parallel to m.

The converse is: :if two alternate exterior angles are congruent, then l is parallel to m".

Therefore, l || m.

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Answer/Step-by-step explanation:

1. YES.

Converse: If same side interior angles are supplementary, then l || m. (Same side interior angles)

Since the sum of the two same side interior angles, 65° and 115°, equals 180°, therefore, l || m.

2. YES.

Converse: if two angles angles are a linear pair, they are supplementary, therefore l || m. (Linear pair)

Thus,

128° + 53° = 180°.

3. YES.

Converse: if two angles are corresponding angles and congruent, therefore l || m. (Corresponding angles).

Thus,

The indicated angles which are equal to 90°, are corresponding angles therefore, l || m.

4. YES

Converse: if two alternate exterior angles are congruent, then l || m. (Alternate exterior angles)

Thus, the two exterior angles are congruent, therefore l || m.

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