perpendicular postulate definition geometry

The Converse of Corresponding Angles Theorem This theorem is also termed as 'corresponding angles postulate'.

When the transversal intersects two 'non-parallel lines', the corresponding angles are NOT congruent.Īccording to the corresponding angles theorem, the statement “ If a line intersects two parallel lines, then the corresponding angles are congruent (equal)” is true either way.

Corresponding angles formed by the transversal that intersects two 'parallel lines' are angles that are congruent.

Corresponding angles are NOT always congruent.

they are on the same side of the transversal andīy this definition, angles ∠1 and ∠2 in the above figure form a pair of corresponding angles.

one of them is interior and the other is exterior.

We define corresponding angles mathematically as follows: 'A pair of angles formed by two parallel lines and a transversal are said to be the corresponding angles if and only if Therefore, we can say that angles ∠1 and ∠2 are corresponding angles.

Hence, our corresponding angles definition seems to be justified. From the diagram, we can see that angles 1 and 2 are occupying the same relative position - the upper right side angles in the intersection region.The corresponding angles definition tells us that when two parallel lines are intersected by a third one ( transversal), the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other.Īccording to geometry, and the definition of the corresponding angles, we can say that:

Perpendicular postulate definition geometry