Notes: Rhombus
A rhombus is a parallelogram with adjacent sides equal. In addition to having all the
properties of a parallelogram, the rhombus has several other properties.
If you are given a rhombus ABCD then:
Property
Meaning
(1) all properties of the parallelogram are true
(1) see properties on page 1
(2) all sides are congruent
(2) AB ⇠
= BC ⇠
= DC ⇠
= AD
(3) the diagonals bisect the opposite angles
(3) m\DAC ⇠
= m\BAC
m\DCA ⇠
= m\BCA
m\ADB ⇠
= m\CDB
m\ABD ⇠
= m\CBD
(4) the diagonals are perpendicular to each other
(4) DB ? AC at E
Practice Problems: Rhombus
Use the properties in the notes section to help you solve the following problems.
(1) In the accompanying diagram of a rhombus CDEF , diagonal F D is drawn and
m\E = 40 . Find m\CF D.
(2) In rhombus ABCD, AB = (6x
3) and BC = (4x + 7). Find x.
(3) The lengths of the diagonals of a rhombus are 6 and 8. What is the length of a side
of a rhombus?
(4) In rhombus ABCD, diagonal DB is congruent to side AD. What is the measure of
\A?
(5) If the lengths of the diagonals of a rhombus are 10 and 24, find the length of one side
of the rhombus.
(6) In the accompanying diagram of rhombus ABCD, m\ABD = 50 . Find m\A.