GEOMETRY: Chapter 6
6.3: Show that a Quadrilateral is a
Parallelogram
Theorem 6.6:
If both pairs of opposite sides of a
quadrilateral are congruent, then the
quadrilateral is a parallelogram.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 522.
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.
Ex.1:
The figure shows part of a stair railing. Explain how you
know the support bars MP  NQ are parallel.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 523.
Ex.1:
The figure shows part of a stair railing. Explain how you
know the support bars MP  NQ are parallel.
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.
Theorem 6.8:
If an angle of a quadrilateral is
supplementary to both of its consecutive
angles, then the quadrilateral is a
parallelogram.
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.
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.
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.
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.
Ex. 3:
For what value of x is quadrilateral RSTU a
parallelogram?
Images taken from: Geometry. McDougal Littell: Boston, 2007. P.524.
Ex. 3:
For what value of x is quadrilateral RSTU a
parallelogram?
Answer: 8
Images taken from: Geometry. McDougal Littell: Boston, 2007. P.524.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 525.
Ex. 4: Show that FGHJ is a parallelogram.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 525.
Ex. 4: Show that FGHJ is a parallelogram.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 525.
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!