Download Prove ABCD is a parallelogram

Geometry
Notes 10-3:
Proving a Quadrilateral is a Parallelogram
A quadrilateral is a parallelogram if any of the following can be proven true.
1. Both pairs of opposite sides are parallel.
2. Both pairs of opposite sides are congruent.
3. Two opposite sides are congruent and parallel.
4. The diagonals bisect each other
5. Both pairs of opposite angles are congruent.
Ex. 1:
Given: Quadrilateral ABCD
Prove: ABCD is a parallelogram
Statements
Reasons
1. Quadrilateral ABCD
1. Given
2.
2. Given
3.
3. Given
C
B
1
2
A
D
Ex. 2 The coordinates of the vertices of quadrilateral
ABCD are A(-1, 4), B(1,0), C(-2,-6), and D(-4,-2).
Prove the quadrilateral is a parallelogram.
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Ex. 3 Given: Quadrilateral ABCD
Statements Reasons
1. quadrilateral ABCD
1. given
2. given
3. given
Prove ABCD is a parallelogram
D
C
F
E
A
B
4. Given: F(-7,3), G(-3,2), H(0,-4) and J(-4,-3) are the vertices of a quadrilateral.
Prove: FGHJ is a parallelogram.
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