1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard IX
Mathematics
Median of Triangle
In a rhombus ...
Question
In a rhombus
A
B
C
D
, the altitude from
D
to the side
B
bisects
A
B
. Find the angles of the rhombus.
Open in App
Solution
From the figure consider
D
P
bisects the side
A
B
at point
P
Construct a line at
B
D
Consider
△
A
M
D
and
△
B
M
D
We know that
M
is the midpoint of
A
B
A
M
=
B
M
from the figure we know that
∠
A
M
D
=
∠
B
M
D
=
90
o
M
D
is common ie
M
D
=
M
D
By SAS congruency criterion
△
A
M
D
≅
△
B
M
D
A
D
=
B
D
(c.p.c.t)
We know that the sides of a rhombus are equal
so we get
A
D
=
A
B
It can be written as
A
D
=
A
B
=
B
D
We know that
△
A
D
B
is an equilateral triangle
so we get
∠
A
=
60
o
we know that
∠
B
+
∠
A
=
180
o
∠
B
=
180
o
−
∠
A
∠
B
=
180
o
−
60
o
∠
B
=
120
o
We know that
∠
D
=
∠
B
=
120
o
Therefore the angles are
∠
C
=
∠
A
=
60
o
and
∠
D
=
∠
B
=
120
o
Suggest Corrections
0
Similar questions
Q.
In a rhombus ABCD, the altitude from D to the side AB bisects AB. Find the angles of the rhombus.