Best Answer

If two lines are cut by a transversal to form pairs of congruent corresponding angles, congruent alternate interior angles, or congruent alternate exterior angles, then the lines are parallel.

Q: What is the converse of parallel lines conjecture?

Write your answer...

Submit

Still have questions?

Continue Learning about Geometry

A transversal is simply any line that passes through two or more coplanar lines each at different points. So picture, if you will, two lines that are clearly not parallel. I can easily construct a transversal that passes through them. HOWEVER, if two parallel lines are intersected by a transversal, then the corresponding angles are congruent. This is called the transversal postulate. If the corresponding angles are congruent, than the lines are parallel. This is the converse of the first postulate. So, the answer to your question is NO, unless the corresponding angles are congruent.

no parallel lines

parallel lines are diagonal lines or increasing lines

Euclid's parallel postulate.

Skew lines are not parallel. Parallel lines are across from each other in some way and are exactly parallel.

Related questions

postulate theorems tell that the lines are parallel, but the converse if asking you to find if the lines are parallel.

If a transversal intersects a pair of lines and the alternate angles are congruent, the lines are parallel.

when two lines are cut by a transversal so that the corresponding angles are congruent, the the lines are parallel

Parallel lines intercept congruent arcs on a circle. More explanation: Parallel lines never interSECT but they can interCEPT Congruent arcs means that the two arcs would have the same measure of the arcs.

A transversal is simply any line that passes through two or more coplanar lines each at different points. So picture, if you will, two lines that are clearly not parallel. I can easily construct a transversal that passes through them. HOWEVER, if two parallel lines are intersected by a transversal, then the corresponding angles are congruent. This is called the transversal postulate. If the corresponding angles are congruent, than the lines are parallel. This is the converse of the first postulate. So, the answer to your question is NO, unless the corresponding angles are congruent.

When two lines are parallel, then they do not intersect.

If they were not actually parallel then they would not be parallel lines!

it has parallel lines

no parallel lines

parallel lines are diagonal lines or increasing lines

= parallel + perpendicular As such no, perpendicular lines do not naturally have parallel lines. However...connect the lines in the symbols below. ++ ++ And you'll have 4 perpendicular lines, and 4 parallel lines.

No, parallel lines do not intersect, and never will.