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Conjecture: m  B = 2(m  A)

7. Conjecture: m  B = 2(m  A). B. D. A. C. B. 30 . E. x. C. A. D. From HW # 6. Given:. 1. x = 15. Find the measure of the angle marked x. x. From HW # 6. x = 15. 2. A. D. B. C. 63 . 63. 41. 104. A. D. B. C. 63 . 63. 41. 104. A. D. B. C. 63 . .

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Conjecture: m  B = 2(m  A)

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  1. 7. Conjecture: mB = 2(mA) B D A C

  2. B 30 E x C A D From HW # 6 Given: 1. x = 15 Find the measure of the angle marked x.

  3. x From HW # 6 x = 15 2.

  4. A D B C 63 63 41 104

  5. A D B C 63 63 41 104

  6. A D B C 63  104

  7. A D B C 63 41  76 104 63 D

  8. 14 C E F D B A

  9. From HW # 6 5. In the diagram, triangle ABC is isosceles with base , E is the midpoint of , and . Prove that triangle DEF and triangle CDF are isosceles. C D F A B E

  10. From HW # 6 5. In the diagram, triangle ABC is isosceles with base , E is the midpoint of , and . Prove that triangle DEF and triangle CDF are isosceles. Outline of proof: 1. A B (isosceles triangle theorem) C D F A B E

  11. From HW # 6 5. In the diagram, triangle ABC is isosceles with base , E is the midpoint of , and . Prove that triangle DEF and triangle CDF are isosceles. Outline of proof: 1. A B (isosceles triangle theorem) 2. AE  EB (definition of midpoint) C D F A B E

  12. From HW # 6 5. In the diagram, triangle ABC is isosceles with base , E is the midpoint of , and . Prove that triangle DEF and triangle CDF are isosceles. Outline of proof: 1. A B (isosceles triangle theorem) 2. AE  EB (definition of midpoint) 3. ADE and BFE are congruent right angles C D F A B E

  13. From HW # 6 5. In the diagram, triangle ABC is isosceles with base , E is the midpoint of , and . Prove that triangle DEF and triangle CDF are isosceles. Outline of proof: 1. A B (isosceles triangle theorem) 2. AE  EB (definition of midpoint) 3. ADE and BFE are congruent right angles 4. ADE BFE (AAS) C D F A B E

  14. From HW # 6 5. In the diagram, triangle ABC is isosceles with base , E is the midpoint of , and . Prove that triangle DEF and triangle CDF are isosceles. Outline of proof: 1. A B (isosceles triangle theorem) 2. AE  EB (definition of midpoint) 3. ADE and BFE are congruent right angles 4. ADE BFE (AAS) 5. DE  EF and AD  BF (CPCTC) C D F A B E

  15. From HW # 6 5. In the diagram, triangle ABC is isosceles with base , E is the midpoint of , and . Prove that triangle DEF and triangle CDF are isosceles. Outline of proof: 1. A B (isosceles triangle theorem) 2. AE  EB (definition of midpoint) 3. ADE and BFE are congruent right angles 4. ADE BFE (AAS) 5. DE  EF and AD  BF (CPCTC) 6. DEF is isosceles (definition of isosceles ) C D F A B E

  16. From HW # 6 5. In the diagram, triangle ABC is isosceles with base , E is the midpoint of , and . Prove that triangle DEF and triangle CDF are isosceles. Outline of proof: 1. A B (isosceles triangle theorem) 2. AE  EB (definition of midpoint) 3. ADE and BFE are congruent right angles 4. ADE BFE (AAS) 5. DE  EF and AD  BF (CPCTC) 6. DEF is isosceles (definition of isosceles ) 7. DC  FC (subtraction post, AC – AD = BC – BF) C D F A B E

  17. From HW # 6 5. In the diagram, triangle ABC is isosceles with base , E is the midpoint of , and . Prove that triangle DEF and triangle CDF are isosceles. Outline of proof: 1. A B (isosceles triangle theorem) 2. AE  EB (definition of midpoint) 3. ADE and BFE are congruent right angles 4. ADE BFE (AAS) 5. DE  EF and AD  BF (CPCTC) 6. DEF is isosceles (definition of isosceles ) 7. DC  FC (subtraction post, AC – AD = BC – BF) 8. CDF is isosceles. C D F A B E

  18. From HW # 6 6. Think about how you would prove that the altitudes to the legs of an isosceles triangle are congruent.

  19. 7. Conjecture: mB = 2(mA) B D A C

  20. Use Geometer’s Sketchpad to construct quadrilateral ABCD in which AB is parallel to CD and BC is parallel to AD.

  21. Quadrilaterals

  22. A parallelogram is a quadrilateral with both pairs of opposite sides parallel. A square is a rhombus and a rectangle. Definitions A rhombus is a parallelogram with one pair of adjacent sides congruent. A rectangle is a parallelogram with one right angle.

  23. bases legs A trapezoid is a quadrilateral with exactly one pair of sides parallel. An isosceles trapezoid is a trapezoid with the two non-parallel sides congruent. Base angles (there are two pairs)

  24. HW #7 Fill in the chart (question 5) on the HW 7 handout. Begin work on the rest of the problems. You will have all period on Monday to complete it.

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