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Chapter 2

Chapter 2. Section 5 Perpendicular lines. The box shows you the right angle. Define: Perpendicular lines ( ^ ). Two lines that intersect to form right or 90 o angles. Remember all definitions are Biconditionals : If two lines are perpendicular then they form right angles

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Chapter 2

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  1. Chapter 2 Section 5 Perpendicular lines

  2. The box shows you the right angle Define: Perpendicular lines (^) • Two lines that intersect to form right or 90o angles Remember all definitions are Biconditionals: If two lines are perpendicular then they form right angles If two lines form right angles then they are perpendicular

  3. Perpendicular Line Theorems • If two lines are perpendicular, then they form congruent adjacent angles • If two lines form congruent adjacent angles, then they are perpendicular

  4. t 2 1 r Hypothesis conclusion reason Perpendicular Line Theorems Given: r^ t Prove: <1 @ <2 • If two lines are perpendicular, then they form congruent adjacent angles None r^ tgiven If r^ t then m<1= 90o & m<2 = 90o def of perpendicular lines If m<1= 90o & m<2 = 90o transitive prop / substitution then m<1 = m<2 If m<1= m<2 then <1 @ <2 def of congruent angles

  5. 2 1 Define: Linear Pair of Angles • Two adjacent angles whose exterior sides are opposite rays. Angles 1 and 2 are a linear pair.

  6. t 2 1 r Hypothesis conclusion reason Perpendicular Line Theorems Given: R1 @ R2 Prove: r^ t • If two lines form congruent adjacent angles, then they are perpendicular None R1 @R2 or mR1 = mR2given If R1 and R<2 are a linear pair then mR1 + mR2 = 180o Angle addition post If mR1 = mR2 and mR1 + mR2 = 180o then 2 (mR1) = 180o substitution If 2 (mR1) = 180o then mR1 = 90o Division property If mR1 = 90o then r^ t Def of ^ lines

  7. 2 1 Define: Perpendicular Pair of Angles • Two adjacent acute angles whose exterior sides are perpendicular. Angles 1 and 2 are a perpendicular pair.

  8. A X 2 1 B C Perpendicular Pair Theorem • If two angles are a perpendicular pair, then the angles are complementary Given: R1 and R2 are a perpendicular pair Prove: R1 and R2 are complementary angles

  9. Hypothesis conclusion reason A X 2 then BA ^ BC 1 B If BA ^ BC C Proof of ^ Pair Theorem Given: R1 and R2 are a perpendicular pair Prove: R1 and R2 are complementary angles None R1 and R2 are a ^ pairgiven If R1 and R2 are a ^ pair Def of ^ pair then mRABC = 90o Def of ^ lines If X is in the interior of RABC then mRABC = mR1 +mR2 Angle addition postulate If mRABC = mR1 +mR2 and mRABC = 90o then mR1 +mR2 = 90o Transitive property or substitution If mR1 +mR2 = 90o then R1 & R2 are comp. R<‘s Def of comp. R‘s

  10. summary Definition of ^ ^ 90 or right ^ line theorems ^ 2 lines forming @ adjacent R’s ^ pair theorem- ^ pair complementary R’s

  11. Practice work • P 58 we 1-25all

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