Section 2.5 – Conjectures That Lead to Theorems

Vertical angles – the opposite angles formed by 2 intersecting lines.

Ex] and 2 are vertical angles

Inductive reasoning – the process of forming conjectures that are based on observations.

Theorem] if 2 angles form a pair of vertical angles, then they are congruent.

Or

Vertical angles are congruent

Theorem] Reflection across two parallel lines is equivalent to a translation of twice the distance between the lines and in a direction perpendicular to the lines.

Congruent Supplements Theorem

If two angles are supplements of congruent angles, then the two angles are congruent.

By proving a theorem, the statement is true for all possible cases. A conjecture may be true for only one or a few cases, but possibly not all cases.