Download Geometry 6-3 Tests for Parallelograms

Geometry 6-3 Tests for Parallelograms
Last time we learned about parallelograms and their
properties. If we know a quadrilateral is a parallelogram, we
discovered several interesting properties. This time we will
using these properties to determine if a quadrilateral is a
parallelogram. Most of our theorems this time will be the
converses of our theorems from last time.
We already know one certain way to tell if we have a
parallelogram. If both sets of opposite sides are parallel,
then the definition tells us we have a parallelogram.
Determine whether the quadrilateral is a parallelogram.
Justify your answer.
12
5
5
No - doesn't fit any thm.
12
14
Theorem 6.10: If both pairs of opposite angles of a quad are
congruent, then the quad is a parallelogram.
Theorem 6.11: If the diagonals of a quad bisect each other,
then the quad is a parallelogram.
Theorem 6.12: If one pair of opposite sides of a quad is both
parallel and congruent, then the quad is a parallelogram.
Find the value of each variable so that the quad is a
4w + 3
3z - 1
110
Yes - Thm 6.9.
120
60
14
Theorem 6.9: If both pairs of opposite sides of a quad are
congruent, then the quad is a parallelogram.
110
Top and bottom are equal. Since
consecutive interior angles are supp, top
and bottom are also parallel.
Yes - Thm 6.12.
Determine whether the quad is a parallelogram. Use the
Distance Formula to decide.
A
A(3,3), B(8,2), C(6,-1), D(1,0)
B
AD = (3-1)2 + (3-0)2 = 4 + 9 = 13
BC = (8-6)2 + (2- -1)2 = 4 + 9 = 13
D
AB = (3-8)2 + (3-2)2 = 25 + 1 = 26
CD = (6-1)2 + (-1-0)2 = 25 + 1 = 26
Since AD = BC and AB = CD, then ABCD is a
parallelogram (Thm 6.9).
C
2z + 3
6w - 2
56
4y + 4
5y - 26
7x
7x = 56
x=8
5y - 26 = 4y + 4
y = 30
.
3z - 1 = 2z + 3
z=4
6w - 2 = 4w + 3
2w = 5
w = 2.5