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6-2 Properties of Parallelograms

6-2 Properties of Parallelograms. L.E.Q. How do you use relationships involving sides, angles, diagonals, and transversals of parallelograms?. You can use what you know about parallel lines and transversals to prove some theorems about parallelograms. Theorem 6-1: Opposite Sides.

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6-2 Properties of Parallelograms

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  1. 6-2 Properties of Parallelograms L.E.Q. How do you use relationships involving sides, angles, diagonals, and transversals of parallelograms?

  2. You can use what you know about parallel lines and transversals to prove some theorems about parallelograms.

  3. Theorem 6-1: Opposite Sides • Opposite sides of a parallelogram are congruent.

  4. What are Consecutive Angles? • Angles of a polygon that share a common side of the polygon.

  5. Example 1: Using Consecutive Angles. • Find

  6. Theorem 6 – 2: Parallelogram Opposite Angles Theorem • Opposite angles in a parallelogram are congruent.

  7. Example 2: Using Algebra. • Find the value of x in PQRS. Then find QR and PS.

  8. Theorem 6 – 3: Parallelogram Diagonals Theorem • The diagonals of a parallelogram bisect each other.

  9. Example 3: Using Algebra. • Solve a system of linear equations to find the values of x and y. Then find AE, EC, BE, and ED.

  10. Find the values of a and b.

  11. Theorem 6 – 4: Three or More Parallel Lines Theorem • If 3 or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

  12. Example 4: Parallel Lines and Transversals. • In the figure below, • Find EH.

  13. Homework: • Pgs. 297-300 #s 2-16, 24-32, 44-52 even

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