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##### 2.5 – Conjectures that lead to Theorems

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**REMEMBER?**• Theorem • A statement that has been proven to be true (using deduction) • Proof • A convincing argument (using postulates, theorems and definitions) that something is true**PROOFS**• Any definition, postulate or theorem that we learn (or have learned) is able to be used in a proof!**Theorems**• Vertical Angles • The opposite angles formed by two intersecting lines • Vertical Angle Theorem • If two angles form a pair of vertical angles, then they are congruent**What do I do?**• The question you need to ask at this point is 1: do the angles add up to 180°? OR 2: are the angles congruent? Then, do they want to know “x” or the angle or both?**Case 1**They are equal because they are vertical (2x+70)° (7x-55)°**Answers**(7x-55)° = (2x+70)° 5x=125 x=25 The angles would both be 7(25)-55=2(25)+70= 120° each**Case 2**• They add up to 180° because they are a linear pair (2x+70)° (2x+10)°**Answers**(2x+10)° + (2x+70)° = 180° 4x+80 = 180 4x = 100 X = 25 But what are the angles?**One of them is**2(25)+10 = 60° And the other is 2(25)+70 = 120° Because I can plug in 25 for x.