Two parallel lines intersected by a common transversal form eight angles
If the red lines are NOT parallel, the angles types that are still congruent are;
Vertical angles
The reason vertical angles are the only correct option is as follows:
According to vertical angles theorem, the vertical opposite angles which are the angles formed when two lines cross are always congruent
Therefore, given that the lines still crosses when they are no longer parallel, the vertical angles are still congruent
Linear pair angles are angles that sum to 180°. By observation, the linear pair are initially not congruent
- Same-side interior angles:
The same side interior angles are the angles located on the same side of the transversal, on the interior area of the parallel lines
The same side interior angles between parallel lines are always supplementary, and can only be congruent when the red lines are parallel and perpendicular to the transversal. By observation the same side interior angles are not congruent
- Alternate interior angles:
By alternate interior angles theorem, the alternate interior angles formed between two parallel lines having a common transversal are always congruent. Therefore, when the red lines are not parallel, the alternate interior angles are not parallel
- Same side exterior angles:
Similar to the same side interior angles, the same side exterior angles are only congruent when the red lines are parallel and perpendicular to the transversal. Therefore, when the red lines are not parallel, the same side exterior angles will not be congruent
- Alternate exterior angles:
According to the alternate exterior angles theorem, the alternate exterior angles formed between two parallel lines having a common transversal are congruent. Therefore, when the red lines are not parallel, the alternate exterior angles will not still be congruent
According to corresponding angles theorem, the corresponding angles formed between two parallel lines intersected by a common transversal are congruent
Therefore, if the red lines are not parallel, the corresponding angles will not still be congruent
Therefore, the angle types that are still congruent when the red lines ae not parallel are the vertical angles
Learn more about angles formed between parallel lines here:
https://brainly.com/question/1751268
