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GEOMETRY: Chapter 6

GEOMETRY: Chapter 6. 6.3: Show that a Quadrilateral is a Parallelogram. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Theorem 6.6:. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 522. Theorem 6.7:.

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GEOMETRY: Chapter 6

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  1. GEOMETRY: Chapter 6 6.3: Show that a Quadrilateral is a Parallelogram

  2. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Theorem 6.6: Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 522.

  3. Theorem 6.7: If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 522.

  4. Ex.1: Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 523.

  5. Ex.1: Answer: MP=NQ and MN=PQ, so MNQP is a parallelogram. Therefore, MP (bar on top) ll NQ. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 523.

  6. Theorem 6.8: If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram.

  7. Theorem 6.9: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 523.

  8. Theorem 6.10: If one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 523.

  9. Ex. 2: Suppose you place two straight, narrow strips of paper of equal length on top of two lines of a sheet of notebook paper. If you draw a segment to join their left ends and a segment to join their right ends, will the resulting figure be a parallelogram? Explain.

  10. Ex. 2: Suppose you place two straight, narrow strips of paper of equal length on top of two lines of a sheet of notebook paper. If you draw a segment to join their left ends and a segment to join their right ends, will the resulting figure be a parallelogram? Explain. Answer: Yes, Since AB=CD, you know that AB is congruent to CD. The segments are parallel since the lines on the notebook paper are parallel. So, by Theorem 8.9, ABCD is a Parallelogram.

  11. Ex. 3: For what value of x is quadrilateral RSTU a parallelogram? Images taken from: Geometry. McDougal Littell: Boston, 2007. P.524.

  12. Ex. 3: For what value of x is quadrilateral RSTU a parallelogram? Answer: 8 Images taken from: Geometry. McDougal Littell: Boston, 2007. P.524.

  13. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 525.

  14. Ex. 4: Show that FGHJ is a parallelogram. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 525.

  15. Ex. 4: Show that FGHJ is a parallelogram. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 525.

  16. 6.3, p. 342, #2-7 all, 9-14 all, 17, 18, 19 (15 questions) Ch. Review p. 382-383 #1-12 all Ch. 6.1-6.3 Quiz next class!

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