Question

Alternate interior angles have one common ---

Answer 1

Hint: Here we will use the property of alternate interior angle. If two parallel lines are transected by a third line, the angles which are inside the parallel lines and on alternate sides of the third line are called alternate interior angles.

Complete step-by-step answer:
Alternate interior angles are the angles formed when a transversal intersects two coplanar lines. Any two intersecting lines must lie in the same plane, and therefore be coplanar. They lie on the inner side of the parallel lines but on the opposite sides of the transversal. The transversal crosses through the two lines which are Coplanar at separate points. These angles represent whether the two given lines are parallel to each other or not.
If these angles are equal to each other then the lines crossed by the transversal are parallel and congruent. Sum of the angles formed on the same side of the transversal which are inside the two parallel lines is always equal to \[180^\circ \]. In the case of non-parallel lines, alternate interior angles don’t have any specific properties.
Therefore, Alternate interior angles have one common arm on the opposite sides of the transversal line.

Note: Two angles are said to be adjacent when they share a common side and a vertex. Vertically opposite angles are the angles formed opposite to each other when two lines intersect. If a transversal crosses the set of parallel lines, the alternate interior angles are congruent. If the alternate interior angles produced by the transversal line on two coplanar are congruent, then the two lines are parallel to each other. Two objects are congruent if they have the same dimensions and shape.