Geometry Proving Quadrilateral are Parallelograms
Proving that Quadrilaterals are Parallelograms 1. by definition… If the opposite sides of a quadrilateral are parallel, then it is a parallelogram. A
A
B
B 66
114
66 D
C
D
114 C
2. If the opposite sides of a quadrilateral are congruent, then it is a parallelogram. A
7 cm
A
B
B
5 cm
D
C
D
5 cm
7 cm
C
3. If the opposite angles of a quadrilateral are congruent, then it is a parallelogram. A
B
D
C
4. If an angle of a quadrilateral is supplementary to both of its consecutive angles, then it is a parallelogram. A A B B (180 - x)
x D
x
(180 - x)
66 C
66
114
D
114 C
5. If the diagonals of a quadrilateral bisect each other, then it is a parallelogram. A
A
B
3.5 cm M
M 5.2 cm D
B
C
D
5.2 cm
3.5 cm C
6. If one pair of opposite sides of a quadrilateral is both congruent and parallel, then it is a parallelogram. A
7 cm
A
B
B
114ď‚°
66ď‚°
D
C
D
7 cm
C