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2-6: Verifying Angle Relationships

2-6: Verifying Angle Relationships . Expectations: L4.3.1: Know the basic structure of an “If, then” proof. G1.1.1: Solve multi-step problems and construct proofs involving vertical angles, linear pairs of angles, supplementary angles, complementary angles and right angles.

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2-6: Verifying Angle Relationships

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  1. 2-6: Verifying Angle Relationships Expectations: L4.3.1: Know the basic structure of an “If, then” proof. G1.1.1: Solve multi-step problems and construct proofs involving vertical angles, linear pairs of angles, supplementary angles, complementary angles and right angles. G1.1.6: Recognize Euclidean geometry as an axiom system. Know the key axioms and understand the meaning of and distinguish between undefined terms (e.g., point, line, and plane), axioms, definitions, and theorems. 2-6: Verifying Angle Relationships

  2. Supplement Theorem(Linear Pair Property) • If 2 angles form a linear pair, then they are supplementary. 2-6: Verifying Angle Relationships

  3. Equivalence Property of Angle Congruence • Congruence of angles is ________, • ___________ and ____________. 2-6: Verifying Angle Relationships

  4. ∠A is supplementary to ∠B and ∠B is congruent to ∠C. What can be said about ∠A and ∠C? 2-6: Verifying Angle Relationships

  5. Congruent Supplements Theorem • If 2 angles are supplementary to the same angle or congruent angles then the angles are _________ to each other. 2-6: Verifying Angle Relationships

  6. Given: ∠1 is supplementary ∠2 and ∠3 supplementary ∠2 • Prove: ∠1≅∠3 2-6: Verifying Angle Relationships

  7. Congruent Complements Theorem • If 2 angles are complementary to the same angle or congruent angles then the angles are _________ to each other. 2-6: Verifying Angle Relationships

  8. Make a conclusion based on: • ∠1 ≅∠3 , ∠1 complementary ∠2 and • ∠3 complementary ∠4 2-6: Verifying Angle Relationships

  9. Right Angle Congruence Theorem • All right angles are ____________. 2-6: Verifying Angle Relationships

  10. Given ∠A and ∠B are right angles. • Prove : ∠A ≅∠B 2-6: Verifying Angle Relationships

  11. Vertical Angle Theorem • If 2 angles are vertical angles, then they are ____________. 2-6: Verifying Angle Relationships

  12. Perpendicular Lines Theorem • If two lines are perpendicular, then they form _______________. 2-6: Verifying Angle Relationships

  13. Solve for x 6x+10 9x-17 2-6: Verifying Angle Relationships

  14. Determine the measure of each angle if m∠1=5x+11 and m∠2=8x-1. 1 2 4 3 • 31, 31 • 31, 59 • 31, 149 • 41.95, 48.25 • 76.4, 103.6 2-6: Verifying Angle Relationships

  15. What is the difference of the measures of angles 1 and 2 in the diagram below if m∠1 = 8x + 4 and m∠2 = 12x – 8, rounded to the nearest whole number? • 0 • 3 • 6 • 9 • 25 ∠1 ∠2 2-6: Verifying Angle Relationships

  16. Assignment • pages 110 -114, • #16 - 32 (evens), 42, 44 2-6: Verifying Angle Relationships

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