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Geometry Postulates and Theorems

Learn about important postulates and theorems in geometry, including the properties of angles, linear pairs, and perpendicular lines.

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Geometry Postulates and Theorems

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  1. Week 1 Warm Up 10.18.11 State the postulate or theorem: 1) If 3 + 4 = 7, then 7 = 3 + 4, 2) If 2x + 5 = 17, then 2x = 12. 3) If ∠A and ∠B are vertical angles, then ∠A ≅ ∠B.

  2. Theorem 3.1 Ex g⊥ h

  3. Given: ∠ 1 ≅ ∠ 2 Ex 1 Prove T3.1 Given: ∠ 1 and ∠ 2 are linear pairs 2 1 Prove: g ⊥ h ∠ 1 ≅ ∠ 2 Given ∠ 1 and ∠ 2 are linear pairs Given m∠ 1 + m∠ 2 = 180º Definition of Linear Pairs m∠ 1 = m∠ 2 Definition of congruent angles m∠ 1 + m∠ 1 = 180º Substitution property of equality 2m∠ 1 = 180º Simplify m∠ 1 = 90º Division property of equality Substitution property of equality m∠ 2 = 90º ∠ 1and ∠ 2 are right angles Definition of right angles g ⊥ h Definition of perpendicular lines

  4. Theorem 3.2 Ex 90º

  5. Theorem 3.3 90º Ex

  6. Theorem 3.3 90º 90º Ex 90º 90º

  7. What can you conclude?: j ⊥k Ex 2 k 8 9 j 7 10 1) ∠ 7 and ∠ 8 are complementary 2) ∠ 9 is a right angle 3) 4)

  8. Review A _______ is a line that intersects two or more coplanar lines. Do: 1 What is the value of x? 65º x Assignment: Handout - Section 3.2 B

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