Parallelogram
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Four Theorems to Prove Quadrilaterals are Parallelograms
Name _________________________________ Date ___________________ Period _______
Parallelogram A parallelogram is a quadrilateral with two pairs opposite sides being parallel ABCD is a parallelogram A
D
B
C
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. A
D
B
C
Statements
Reasons
Given: AB ! DC; AD ! BC Prove: ABCD is a parallelogram A
D
B
C
© iTutoring.com Four Theorems to Prove Quadrilaterals are Parallelograms Pg. 2
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. A
D
B
C
Statements
Reasons
Given: !1 " !3; !2 " !4 Prove: ABCD is a parallelogram A
B
1
4 D
2
3 C
© iTutoring.com Four Theorems to Prove Quadrilaterals are Parallelograms Pg. 3
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. A
B P
D
C
Statements
Reasons
Given: AC and DB bisect each other at point P Prove: ABCD is a parallelogram A
B P
D
C
© iTutoring.com Four Theorems to Prove Quadrilaterals are Parallelograms Pg. 4
If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram. A
D
B
C
Statements
Reasons
Given: AB ! DC and AB ║ DC Prove: ABCD is a parallelogram A
D
B
C
© iTutoring.com Four Theorems to Prove Quadrilaterals are Parallelograms Pg. 5
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.
© iTutoring.com Four Theorems to Prove Quadrilaterals are Parallelograms Pg. 6
Four Theorems to Prove Quadrilaterals are Parallelograms
Name _________________________________ Date ___________________ Period _______
Parallelogram A parallelogram is a quadrilateral with two pairs opposite sides being parallel ABCD is a parallelogram A
D
B
C
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. A
D
B
C
Statements
Reasons
Given: AB ! DC; AD ! BC Prove: ABCD is a parallelogram A
D
B
C
© iTutoring.com Four Theorems to Prove Quadrilaterals are Parallelograms Pg. 2
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. A
D
B
C
Statements
Reasons
Given: !1 " !3; !2 " !4 Prove: ABCD is a parallelogram A
B
1
4 D
2
3 C
© iTutoring.com Four Theorems to Prove Quadrilaterals are Parallelograms Pg. 3
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. A
B P
D
C
Statements
Reasons
Given: AC and DB bisect each other at point P Prove: ABCD is a parallelogram A
B P
D
C
© iTutoring.com Four Theorems to Prove Quadrilaterals are Parallelograms Pg. 4
If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram. A
D
B
C
Statements
Reasons
Given: AB ! DC and AB ║ DC Prove: ABCD is a parallelogram A
D
B
C
© iTutoring.com Four Theorems to Prove Quadrilaterals are Parallelograms Pg. 5
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.
© iTutoring.com Four Theorems to Prove Quadrilaterals are Parallelograms Pg. 6
