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1 Lesson Plan #40 Class: Geometry Date: Monday December 10th, 2012 Topic: Parallelograms Aim: What are some properties of parallelograms? Objectives: 1) Students will know the different ways to prove a quadrilateral is a parallelogram. 2) Students will be able to prove that a quadrilateral is a parallelogram. HW #40: Do Now: 1) Write the definition of a parallelogram 2) Write the definition of a parallelogram as two separate conditionals. 3) What would be a way to prove that a quadrilateral is a parallelogram? PROCEDURE: Write the Aim and Do Now Get students working! Take attendance Give Back HW Collect HW Go over the Do Now Assignment #1: Complete the proof below Given: Quadrilateral π΄π΅πΆπ· with Μ Μ Μ Μ π΄π΅ ≅ Μ Μ Μ Μ πΆπ· and Μ Μ Μ Μ π΄π· ≅ Μ Μ Μ Μ π΅πΆ Prove: ABCD is a parallelogram Plan: Draw Μ Μ Μ Μ π΄πΆ . Prove βπ΄π΅πΆ ≅ βπΆπ·π΄ by π . π . π . ≅ π . π . π . Then use congruent corresponding angles to prove that the opposite sides of ABCD are parallel Statements 1. Quadrilateral π΄π΅πΆπ· 2. Draw Μ Μ Μ Μ π΄πΆ 3. Μ Μ Μ Μ π΄π΅ ≅ Μ Μ Μ Μ πΆπ· π . ≅ π . 4. Μ Μ Μ Μ π΄π· ≅ Μ Μ Μ Μ π΅πΆ π . ≅ π . 5. Μ Μ Μ Μ π΄πΆ ≅ Μ Μ Μ Μ π΄πΆ π . ≅ π . 6. βπ΄π΅πΆ ≅ βπΆπ·π΄ 7. < π΄πΆπ΅ ≅< πΆπ΄π· Μ Μ Μ Μ β₯ π΅πΆ Μ Μ Μ Μ 8. π΄π· 9. < π·πΆπ΄ ≅< π΅π΄πΆ 10. Μ Μ Μ Μ π·πΆ β₯ Μ Μ Μ Μ π΄π΅ 11.π΄π΅πΆπ· is a parallelogram Reasons 1. Given 2. A line segment may be drawn joining 2 points. 3. 4. 5. 6. 7. 8. 9. 10. 11. Assignment #2: Write the theorem that we have just proven above Theorem: 2 Summary of ways to prove a quadrilateral is a parallelogram: To prove that a quadrilateral is a parallelogram, prove any one of the following statements is true: 1) Both pairs of opposite sides are parallel. 2) Both pairs of opposite sides are congruent. 3) One pair of opposite sides are both congruent and parallel. 4) The diagonals bisect each other. 5) Both pairs of opposite angles are congruent. Complete the exercises below: 3 4