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TEQ - Inequalities

TEQ - Inequalities. Write out the theorem or postulate that allows the following conclusions (refer to picture at right). D. a). C. An exterior angle of a triangle is greater than either of its nonadjacent interior angles. B. A. b). A whole is greater than any of its parts.

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TEQ - Inequalities

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  1. TEQ - Inequalities

  2. Write out the theorem or postulate that allows the following conclusions (refer to picture at right). D a) C An exterior angle of a triangle is greater than either of its nonadjacent interior angles B A b) A whole is greater than any of its parts • 2. Write out the reason for the following conclusions. • if A < B and C = D, then A + C < B + D • When equal quantities are added to unequal quantities, their sum is unequal in the same order • if A < B and B < D, then A < D • Transitive postulate of inequalities • c) if A < B and C = D, then A - C < B - D • Subtraction posulate of inequalities

  3. TEQ #3 A Statement Reason 1. Given E 2. Given D B 3. Reflexive postulate C 5. CPCTC Given: 6. Reflexive postulate 8. CPCTC Prove:

  4. Based on the diagram, prove: D C 5. F Statements Reasons 1. 1. GIVEN A E B 2. 2. GIVEN 3. GIVEN 3. 4. Multiplication postulate of inequalities 5. Substitution postulate of inequalities

  5. A D B C E 6. Statement Reason 1. Given 2. Given 3. When equal quantities are added to unequal quantities, their sum is unequal in the same order 4. Partition postulate 5. Substitution postulate of inequalities

  6. Based on the diagram, prove: 7. Statement Reason D 1. Given 2. Given 3. Angles opposite congruent sides of a triangle are congruent E C 4. Substitution Postulate 5. Two lines cut by a transversal that form congruent alternate interior angles are parallel B A

  7. Questions 8 & 9 are based on the diagram above. 8) Which of the following statements must be true? a) 2 1 3 4 b) c) d) 9) Which of the following statements must be true? a) b) c) d)

  8. 11. Statement Reason A 1. Given 2. An exterior angle of a triangle is greater than either of its nonadjacent interior angles 2 3. Transitive postulate of inequalities 1 B D C

  9. 12. 1. Given 2. Given 3. A median extends from a vertex of a triangle to the midpoint of the opposite side 4. A midpoint divides a segment into 2 congruent parts 5. Reflexive postulate 7. CPCTC 8. Two intersecting lines that form congruent adjacent angles are perpendicular

  10. 1. Given 2. Given 3. Perpendicular lines form right angles 4. All right angles are congruent 5. A midpoint divides a segment into 2 congruent parts 6. Reflexive postulate 8. CPCTC

  11. 3. Reflexive postulate 5. CPCTC

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