Lesson 5.6 Power point
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5.6 Proving That a Quadrilateral
is a Parallelogram
Objective:
After studying this section, you will be able to
prove that a quadrilateral is a parallelogram.
Methods to prove quadrilateral
ABCD is a parallelogram
A
D
C
B
1. If both pairs of opposite sides of a
quadrilateral are parallel, then the quadrilateral is
a parallelogram (reverse of the definition).
2. If both pairs of opposite sides of a
quadrilateral are congruent, then the
quadrilateral is a parallelogram (converse of a
property).
3. If one pair of opposite sides of a quadrilateral
are both parallel and congruent, then the
quadrilateral is a parallelogram.
4. If the diagonals of a quadrilateral bisect each
other, then the quadrilateral is a parallelogram
(converse of a property).
5. If both pairs of opposite angles of a
quadrilateral are congruent, then the
quadrilateral is a parallelogram (converse of a
property).
F
E
D
Given: ACDF is a parallelogram
AFB ECD
Prove: FBCE is a parallelogram
A
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B
C
Given:
CAR is isosceles, with base CR
AC BK
C K
Prove: BARK is a parallelogram
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C
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B
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K
Q
Given: Quadrilateral QUAD with
angles as shown
Show that QUAD is a parallelogram
x2
U
5
3x
D
x
3 x x 5 x
2
10
3
15 x 2
A
Given: NRTW is a parallelogram
W
NX TS
WV PR
V
T
X
S
Prove: XPSV is a parallelogram
N
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P
R
Summary
Using one of the methods to prove
quadrilaterals are parallelograms,
create your own problem and show
how it is a parallelogram.
Homework: worksheet