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6-2 Properties of Parallelograms M11.C.1 2.9.11.C

6-2 Properties of Parallelograms M11.C.1 2.9.11.C. Objectives: To use relationships among sides and among angles of parallelograms. To use relationships involving diagonals of parallelograms or transversals. Theorem. Opposite sides of a parallelogram are congruent. Symbol . Example.

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6-2 Properties of Parallelograms M11.C.1 2.9.11.C

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  1. 6-2 Properties of Parallelograms M11.C.1 2.9.11.C Objectives: To use relationships among sides and among angles of parallelograms. To use relationships involving diagonals of parallelograms or transversals.

  2. Theorem Opposite sides of a parallelogram are congruent. Symbol

  3. Example Draw parallelogram PQRS. Find x. QR = 3x – 15 PS = 2x + 3

  4. Vocabulary Consecutive Angles – Angles of a polygon that share a side. They are same-side interior angles, therefore supplementary.

  5. Examples: Using Consecutive Angles Find m∠O.

  6. Theorem Opposite angles of a parallelogram are congruent

  7. Example: Use opposite angles Find the value of x in quadrilateral ABCD. Then find the m∠A

  8. Theorem The diagonals of a parallelogram bisect each other.

  9. Example: Using Diagonals Parallelogram ABCD Diagonals meet at E AE= 3y - 7 EC=2x BE= x + 1 ED= y Find x and y. Find AE, EC, BE, and ED.

  10. Classwork HANDED-IN Pg 297 #1-10, 12-15, 17, 18

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