6.3 Proving That a Quadrilateral is a Parallelogram

1
6.3 Proving That a Quadrilateral is a
Parallelogram

• Chapter 6
• Quadrilaterals

2
6.3 Proving That a Quadrilateral is a
Parallelogram

• Theorem 6-5
• If the diagonals of a quadrilateral bisect
  each other, then the quadrilateral is a
  parallelogram

3
6.3 Parallelograms

• Theorem 6-6
• If one pair of opposite sides of a
  quadrilateral is both congruent and parallel,
  then the quadrilateral is a parallelogram

4
Finding Values

• Find the values of x and y for which MLPN must be
  a parallelogram.

L
P
2y - 7
x 5
y 2
3x
M
N
5
Finding Values

• Find the values of a and c for which PQRS must be
  a parallelogram.

R
Q
a
(a 40)
3c 3
c 1
S
P
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6.3 Parallelograms

• Theorem 6-7
• If both pairs of opposite sides of a
  quadrilateral are congruent, then the
  quadrilateral is a parallelogram.
• Theorem 6-8
• If both pairs of opposite angles of a
  quadrilateral are congruent, then the
  quadrilateral is a parallelogram.

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Is the Quadrilateral a Parallelogram?
95
95
95
x
x
8
Practice

• Pg 307 1-16, 26-29