Lesson 3.2 Proof and Perpendicular Lines. Theorem 3.1  If two lines intersect to form a linear pair of congruent angles, then the lines are  Ex 1 ABC.

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Presentation transcript:

Lesson 3.2 Proof and Perpendicular Lines

Theorem 3.1  If two lines intersect to form a linear pair of congruent angles, then the lines are  Ex 1 ABC D m<ABD = m<DBC and a linear pair, DB AC

Why????? StatementsReasons 1. <1 and <2 are a linear pair <1 and <2 are supplementary3. 4. m<1 + m<2 = m<1 = m< m<1 + m<1 = (m<1) = m<1 = <1 is a right angle h g 1 2

Theorem 3.2  If two sides of two adjacent acute angles are perpendicular, then the angles are complementary.  Ex. 2 H F G J <FGJ is complementary to <JGH

Given: m ⊥ n Prove: <1 and <2 are complementary StatementsReasons 1. m ⊥ n <mpn is a right angle2. 3. m<mpn = m<1 + m<2 = m<mpn4. 5. m<1 + m<2 = <1 and <2 are complementary 6. m n 1 2 p

Theorem 3.3  If 2 lines are perpendicular, then they intersect to form four right angles. m l

Why??? StatementsReasons 1. <1 and <2 are a linear pair1. 2. j ⊥ k Linear Pair Postulate 4. m<1 + m<2 = <1 is a right angle Defn. of right angles m<2 = Given: j ⊥ k, <1 and <2 are a linear pair Prove: <2 is a right angle j k m<2 = <2 is a right angle9.

Examples: Solve for x 1. 60° x ANSWER: 60 + x = x = 30

Example 2 x 55° ANSWER: x + 55 = x = 35

Example 3 27° (2x-9)° ANSWER: 2x – = 90 2x +18 = 90 2x = 72 x = 36

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