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Chapter 8.3 Notes: Show that a Quadrilateral is a Parallelogram

Chapter 8.3 Notes: Show that a Quadrilateral is a Parallelogram. Goal: You will use properties to identify parallelograms. Ways to Prove a Quadrilateral is a Parallelogram Theorem 8.7 :

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Chapter 8.3 Notes: Show that a Quadrilateral is a Parallelogram

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  1. Chapter 8.3 Notes: Show that a Quadrilateral is a Parallelogram Goal: You will use properties to identify parallelograms.

  2. Ways to Prove a Quadrilateral is a Parallelogram • Theorem 8.7: If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. If _____________, then ABCD is a parallelogram. • Theorem 8.8: If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. If _____________, then ABCD is a parallelogram.

  3. Ex.1: In quadrilateral WXYZ, Find Is WXYZ a parallelogram. Explain your reasoning.

  4. Ex.2: An amusement park ride has a moving platform attached to four swinging arms. The platform swings back and forth, higher and higher, unit it goes over the top and around in a circular motion. In the diagram below, represent two of the swinging arms, and is parallel to the ground (line L). Explain why the moving platform AB is always parallel to the ground.

  5. Theorem 8.9: If one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram. If _____________, then ABCD is a parallelogram. • Theorem 8.10: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. If _____________, then ABCD is a parallelogram.

  6. Ex.3: The doorway shown is part of a building in England. Over time, the building has leaned sideways. Explain how you know that SV = TU.

  7. What theorem can you use to show that the quadrilateral is a parallelogram? Ex.4: Ex.5: Ex.6:

  8. For what value of the variable(s) is the quadrilateral a parallelogram? Explain why. Ex.7: Ex.8: 66o yo xo zo

  9. Ex.9: x + 14 5y – 4 2y + 8 3x

  10. Ex.10: (x + 10)o (2x + 20)o Ex.11: Show that quadrilateral ABCD is a parallelogram.

  11. Ex.12: Given: Prove: MJKL is a parallelogram J K M L

  12. Ex.13: Given: Prove: ABCD is a parallelogram F D C A B

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