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6-2 Properties of Parallelograms

6-2 Properties of Parallelograms. Quadrilaterals. In a quadrilateral, opposite sides do not share a vertex and opposite angles do not share a side. In other words, they are ACROSS from each other.

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6-2 Properties of Parallelograms

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  1. 6-2 Properties of Parallelograms

  2. Quadrilaterals • In a quadrilateral, opposite sides do not share a vertex and opposite angles do not share a side. • In other words, they are ACROSS from each other. • Angles of a polygon that share a side are consecutive angles.

  3. Parallelograms • A parallelogram is a quadrilateral with both pairs of opposite sides parallel. Theorem 6-3: If a quadrilateral is a parallelogram, then its opposite sides are congruent. Theorem 6-4: If a quadrilateral is a parallelogram, then its consecutive angles are supplementary. Theorem 6-5: If a quadrilateral is a parallelogram, then its opposite angles are congruent. Theorem 6-6: If a quadrilateral is a parallelogram, then its diagonals bisect each other.

  4. Using Consecutive Angles • What is mP?  Suppose you adjust the lamp so thatmS = 86. What is mR?

  5. Using Algebra to Find Lengths • Solve a system of linear equations to find the values of x and y. What are KM and LN?

  6.  Find the values of x and y. What are PR and SQ?

  7. Parallel Lines and Transversals Theorem 6-7: If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

  8. Using Parallel Lines and Transversals • In the figure, marked lines are parallel, AB = BC = CD = 2, and EF = 2.25. What is EH?  If EF = FG = GH = 6 and AD = 15, what is CD?

  9. 6-3 Proving That a Quadrilateral Is a Parallelogram

  10. Proving a Quadrilateral is a Parallelogram Theorem 6-8: If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Theorem 6-9: If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram. Theorem 6-10: If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Theorem 6-11: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. Theorem 6-12: If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.

  11. Finding Values for Parallelograms • For what value of y must PQRS be a parallelogram?

  12.  For what values of x and y must EFGH be a parallelogram?

  13. Deciding Whether a Quadrilateral Is a Parallelogram Can you prove that the quadrilateral is a parallelogram based on the given information?

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