Theorems 6.1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
Theorem 6.1: If two parallel lines are transected by a third, the alternate interior angles are the same size.
Theorem 6.2: If a line intersects two other lines then the following conditions are equivalent.
Theorem 6.3: The angles in a triangle always add up to 180o.
Theorem 6.4: If two lines are crossed by a third, then the following conditions are equivalent.
Theorem 6.5: Two line segments are congruent if and only if they have the same length.
Theorem 6.6: Two angles are congruent if and only if they have the same size.
Theorem 6.7: (SSS) Two triangles are congruent if and only if their corresponding sides all have the same lengths.T4
Theorem 6.8: (SAS) Two triangles are congruent if and only if two sides and the angles between them in one triangle are congruent to the two sides and the angle between them in the other triangle. T4
Theorem 6.9: Two triangles are similar if and only if the ratios of their corresponding sides are all the same.
Theorem 6.10: (ASA) Two triangles are congruent if and only if two angles and the side between them in one triangle are congruent to two angles and the side between them in a second triangle, then the triangles are congruent.2
Theorem 6.11: (AAS) Two triangles are congruent if and only if two angles and the side next to one of them in one triangle are congruent to two angles and the corresponding side in a second triangle, then the triangles are congruent.