Download Geometry Section 5.3 Show that a Quadrilateral is a Parallelogram If

warm-up after 5.2:
Geometry Section 5.3
Show that a Quadrilateral
is a Parallelogram
1. Find the values of the variables in the parallelogram.
c˚
18
Learning Target:
I can calculate angle measures and segment lengths for
parallelograms and determine if a quadrilateral is a parallelogram.
[G.CO.11]
a = ____
c = ____
b = ____
From Section 5.2 - Properties of Parallelograms
Use the diagram of parallelogram XYZW.
Complete the statement and give a reason for your answer.
If
, then opp. sides //. (defn of
If
, then opp. sides
1. XW ≅ _____
If
, then opp. angles
2. ∠XYZ ≅ _____
If
, then consec.
If
, then diagonals bisect each other.
s supplementary.
If want to prove a quad. is a
,
use the converses of the properties of a
To prove a quadrilateral is a
)
.
:
A. If BOTH pairs of opposite sides are parallel,
then it is a
B. If BOTH pairs of opposite sides are ≅,
then it is a
C. If BOTH pairs of opposite angles are ≅,
then it is a
D. If diagonals bisect each other,
then it is a
E. If ONE pair of opposite sides are parallel and ≅,
then it is a
F. If ONE angle is supplementary to 2 (Same - side) consecutive angles,
then it is a
X
W
Q
3. XQ ≅ _____
Y
Z
4. ∠WYZ ≅ _____
What theorem or definition can you use to show that the quad. is a
1.
2.
?
3. The figure shows part of a stair railing. Explain how you know
the support bars MP and NQ are parallel.
ft
M 2
For what value of x is the quadrilateral a parallelogram?
4.
N
3 ft
3 ft
f
P 2
t
Q
5.
For what value of x is the quadrilateral a parallelogram?
6.