Quadrilateral Family Worksheets - Definitions, Properties Chart, Family Tree And Venn Diagram Page 12
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13Quadrilateral Proofs!
Name___________________________ Date___________ Pd___
Definition of
:
A quadrilateral is a parallelogram both pairs of opposite sides are parallel.
Theorem 6-1:
Parallelogram opposite sides are congruent.
Theorem 6-2:
Parallelogram opposite angles are congruent.
Theorem 6-3:
Parallelogram diagonals bisect each other.
Theorem 6-8:
One pair of opposite sides of a quadrilateral is both congruent and parallel parallelogram.
1. Prove that consecutive angles in a
are supplementary, without
using any of the theorems above.
4. Prove Theorem 6-3, without using any of the theorems above except
Given:
ABCD
Theorem 6-1.
B
A
Prove:
A
and
B
are supplementary,
Given:
ABCD
, where
and
intersect at point
E
.
AC
BD
B
and
C
are supplementary,
Prove:
bisects
, and
bisects
.
AC
BD
BD
AC
C
and
D
are supplementary, and
E
D
and
A
are supplementary.
B
A
C
D
1
2. Prove Theorem 6-1, without using any of the theorems above. (Hint:
E
draw
.)
AC
Given:
ABCD
C
D
Prove:
and
.
AB CD
AD BC
5. Prove Theorem 6-8, without using any of the theorems above.
5
B
A
Given:
and
.
AD BC
AD BC
||
ABCD
Prove:
is a parallelogram.
E
B
A
2
C
D
1
3. Prove Theorem 6-2, without using any of the theorems above.
E
Given:
ABCD
Prove:
and
.
DAB
BCD
ABC
CDA
C
D
B
A
2
3
4
1
E
C
D
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