theorem (triangles ang transversal)

Theorem 6-5 AIP (Alternate Interior Parallel)
--> Given 2 lines cut by a transversal. If a pair of alternate interior angles are congruent, then the lines are parallel.

Theorem 6-6
--> Given 2 lines cut by a transversal. If a pair of coresponding angles are congruent then a pair of corresponding angles are congruent, then a pair of alternate interior angles are congruent.

Theorem 6-7
--> Given 2 lines cut by a transversal. If a pair of corresponding angles are congruent then the lines are parallel.

Theorem 6-8
--> Given 2 lines cut by a transversal. Of a pair pf interior angles on the same side of the transversal are suplementary, the lines are parallel.

Theorem 6-9 The PAI Theorem
--> If 2 parallel lines are cut by a transversal, then the alternate interior angles are congruent.

Corollary 6-9.1 The PCA Corollary
--> If 2 parallel lines are cut by a transversal, then each pair of corresponding angles are congruent.

Corollary 6-9.2
--> If 2 parallel lines are cut by a transversal, the interior angles on the same side of the transversal are suplementary.

6-8 IASP / Consecutive Interior Angles suplementary
6-8.1 CESP/ COnsecutive Exterior Angles Suplementary
AEP/ Alternate Exterior Angles Parallel

Theorem 6-10
--> In a plane, if a line intersects one of two parallel lines in only one point, then it intersects the other.

Theorem 6-11
--> In a plane, if two lines are each parallel to a third line then they are parallel to each other.

Theorem 6-12
--> In a plane, if a line is perpendicular to one of two parallel lines it is perpendicular to one of two parallel lines it is perpendicular to the other.

Theorem 6-13
--> For every triangle, the sum of the measures of the interior angles is 180

6-13.1
--> Given a correspondence between two triangles if two pairs of corresponding angles are congruent, then the 3rd pair of corresponding angles are also congruent.

6-13.2
--> The acute angles of a right triangle are coplementary.

6-13.3
--> For any triangles, the measure of any exterior angles the sum of the two remote interior angles.

theorems (lines and planes)

Theorem 6-1
--> Two parallel lines lie in exactly one plane

Theorem 6-2
--> In a plane, two lines are parallel if they are both perpendicular at the same line.

Theorem 6-3
--> Let L be a line and let P be a point NOT on L. There is at least one line through P parallel to L.

Theorem 6-4
--> If 2 lines are cut by a transversal and one pair of alternate interior angles are congruent, then the other pair of alternate angles are also congruent.