T e ac h i n g T r a n s pa r e n cy
6-4
Properties of Special
Parallelograms
Theorems Properties of Rectangles
THEOREM
If a quadrilateral is
a rectangle, then it
is a parallelogram.
(rect. → )
If a parallelogram
is a rectangle, then
its diagonals are
congruent.
(rect. → diags. )
Theorems
HYPOTHESIS
B
C
A
D
B
C
A
D
ABCD is a
parallelogram.
_
_
AC BD
Properties of Rhombuses
THEOREM
HYPOTHESIS CONCLUSION
If a quadrilateral is a
B
rhombus, then it is a
parallelogram.
(rhombus → )
A
If a parallelogram
B
is a rhombus, then
its diagonals are
perpendicular.
A
(rhombus → diags. ⊥)
If a parallelogram is
B
12
a rhombus, then each
diagonal bisects a pair
8
of opposite angles.
A 7
(rhombus → each diag.
bisects opp. )
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All rights reserved.
CONCLUSION
129
C
ABCD is a
parallelogram.
D
C
_
_
AC ⊥ BD
D
3
6
C
4
5
D
∠1
∠3
∠5
∠7
∠2
∠4
∠6
∠8
Holt McDougal Geometry