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6.2 Properties of Parallelograms

6.2 Properties of Parallelograms

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6.2 Properties of Parallelograms

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  1. 6.2 Properties of Parallelograms Chapter 6 Quadrilaterals

  2. 6.2 Properties of Parallelograms • Theorem 6-1: Opposite sides of a parallelogram are congruent

  3. Consecutive and Opposite Angles • Consecutive Angles: Angles that share a side (Angles that are “next” to each other) • Opposite Angles: Angles that are across from each other in the parallelogram

  4. 6.2 Properties of Parallelograms • Consecutive Angles are Supplementary because they are same-side interior angles

  5. Using Consecutive Angles • Find m<S in RSTW ST and RW are parallel, so <S and <R are what kind of angles? S T 68° W R

  6. 6.2 Properties of Parallelograms • Theorem 6-2: Opposite angles of a parallelogram are congruent

  7. Using Algebra • Find the value of x in PQRS. Then find QR and PS. 3x - 15 R Q S P 2x + 3

  8. Using Algebra • Find the value of y in EFGH. Then find m<E, m<F, m<G, m<H. E F 3y + 37 6y + 4 G H

  9. 6.2 Properties of Parallelograms • Theorem 6-3: The diagonals of a parallelogram bisect each other

  10. Using Algebra • Solve for x and y B C x + 1 2y 3y - 7 x D A

  11. Solve:

  12. Using Algebra • Solve the system of equations to find the values of x and y. Then find AE, EC, BE, and ED. B C x + 1 2x E 3y - 7 y D A