1. UNIT 7 LESSON 4B PROVING PARALLELOGRAMS CCSS G-CO 11: Prove theorems about parallelograms. LESSON GOALS Use properties of parallelograms to prove that a quadrilateral is a parallelogram in a two- column or coordinate plane proof. ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

2. COORDINATE GEOMETRY When a figure is in the coordinate plane you can use: the Distance formula to prove that sides are congruent the slope formula to prove that sides are parallel the midpoint formula to prove the diagonals bisect each other.

3. FORMULAS Distance Formula Slope Formula Midpoint Formula

4. Show that quadrilateral ABCD is a parallelogram (–1, 2) A C (1, – 2) x y B ( 3, 2) (– 3, – 2) D Not on the coordinate plane. EXAMPLE

5. Show that quadrilateral ABCD is a parallelogram (–1, 2) A C (1, – 2) x y B ( 3, 2) (– 3, – 2) D METHOD 1

6. Show that quadrilateral ABCD is a parallelogram (–1, 2) A C (1, – 2) x y B ( 3, 2) (– 3, – 2) D METHOD 2

7. Show that quadrilateral ABCD is a parallelogram (–1, 2) A C (1, – 2) x y B ( 3, 2) (– 3, – 2) D METHOD 3

8. Show that quadrilateral ABCD is a parallelogram (–1, 2) A C (1, – 2) x y B ( 3, 2) (– 3, – 2) D METHOD 4

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