6.5 – Theorems
Theorem 6.15 – The diagonals of a rhombus are perpendicular
Example – AC
BD
Theorem 6.16 – If the diagonals of a parallelogram are perpendicular, then the parallelogram is
a rhombus.
Theorem 6.17 – Each diagonal of a rhombus bisects a pair of opposite angles.
Example - ∠BAC ≅ ∠CAD, ∠ABD ≅ ∠CBD, ∠BCA ≅ ∠DCA, ∠CDB ≅ ∠ADB
A
D
Property
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent
Consecutive angles are supplementary
Diagonals bisect each other
Diagonals are congruent
All four angles are right angles
Diagonals are perpendicular
Diagonal is an angle bisector
All four sides congruent
B
C
Parallelogram
Yes
Yes
Yes
Yes
Yes
Maybe
Maybe
Maybe
Maybe
Maybe
Rectangle
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Maybe
Maybe
Maybe
Rhombus
Yes
Yes
Yes
Yes
Yes
Maybe
Maybe
Yes
Yes
Yes
Square
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes