Using Properties of Parallel Lines

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Presentation transcript:

Using Properties of Parallel Lines Chapter 3 Section 3.5 Using Properties of Parallel Lines

Warm-Up   2x + 4 + 3x – 9 = 180 5x – 5 = 180 5x = 185 x = 37

New Theorems Theorem 3.11: If two lines are parallel to the same line then the lines are parallel to each other p q r If p // r and r // q, then p // q

New Theorems Theorem 3.12: In a plane, if two lines are perpendicular to the same line, then they are parallel to each other m n p If m  p and n  p, then m // n

State the postulate or theorem that allows you to conclude a // b Two lines  to the same line then they are ||

State the postulate or theorem that allows you to conclude a // b Corresponding Angle Postulate.

State the postulate or theorem that allows you to conclude a // b If two lines are || to the same line, then they are || to each other.

Explain how you would show that a // b Explain how you would show that a // b. State any postulates or theorems you would use. If two lines  to the same line then they are || Alternate Exterior angle Converse

Explain how you would show that a // b Explain how you would show that a // b. State any postulates or theorems you would use. a || c – Alt. Int.  Converse b || c – Cons. Int.  Converse a || c – Two lines // to the same line are // to each other

Constructions We will come back to these at a later date Construct a perpendicular thru a given point Copy an angle Construct a parallel thru a given point

Complete the Two Column Proof of Theorem 3.12 Given Def.  Lines Def.  Lines Rt   thm. Corres  Converse