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Geometry B – Notes Section 6.3 Definitions and Theorems involving parallelograms 1. 2. 3. 4. 5. Given: ABCD is a parallelogram Statements Reasons Prove: AGB CGD D C 1 3 5 6 2 G 4 A B Determine which of the figures below are parallelograms. If so, which definition or theorem proves it is a parallelogram. D 60 C D C 120 A B A D C B D 60 120 A B 60 A B C AD BC, 1 2 AB // DC, E is the midpoint of AE A A B B 1 E E 2 C D D C Yesterday we looked at two ways to prove a figure is a parallelogram while graphing. What were those two ways and what formulas did you use? 1. How many times do you use that formula?_____________ 2. How many times do you have to use the formula?______________ A former student said she could prove a figure was a parallelogram by using the midpoint formula only 2 times. Look back at the 5 theorems concerning parallelograms and determine how the midpoint formula could be used. Use the example below to help you. Prove that ABCD is a parallelogram. A(2 , 5) C(3 , -1) B(5 , 9) D(6 , 3) Geometry – Proving a Parallelogram Definition of a parallelogram – A quadrilateral with opposite sides parallel. Diagonals bisects each other Given: Prove: ABCD is a parallelogram A B C D Opposite Sides Congruent Given: Prove: ABCD is a parallelogram A B C D Consecutive angles supplementary Given: Prove: ABCD is a parallelogram A B C D One pair of sides parallel and congruent Given: Prove: ABCD is a parallelogram A B D Opposite angles congruent.- C D D C D C 60 C 120 A B A B A B AD BC, 1 2 AB //A DC, E is the midpoint of AE B A B 1 E E 2 C D D C Below you are going to determine if the figure is a parallelogram. A(2 , 5) C(3 , -1) B(5 , 9) D(6 , 3) Determine which formulas can be use when proving a quadrilateral is a parallelogram based on the following definitions or theorems Opposite Sides Parallel Opposite angles Opposite Sides Diagonals bisect each otherOne pair of sides // and -