Example 6 Is it possible to construct a rhombus ABCD where AC = 6 cm and BD = 7 cm? Justify your answer..
Here, we are given a rhombus
with both diagonals
To construct it,
we will use property of rhombus
In rhombus,
Diagonals are perpendicular bisectors of each other
So, our figure will look like
Here, BD is the perpendicular bisector of AC
So, BD ⊥ AC
and O is the mid-point of AC and BD
∴ OD = OB = (7 𝑐𝑚)/2 = 3.5 cm
To construct it,
we will first draw AC, then perpendicular bisector of AC
Then, we will mark OD = 3.5 cm and OB = 3.5 cm on the perpendicular bisector.
Let’s construct it
.
Steps of construction
1. Draw diagonal AC of length 6 cm
2. Drawing perpendicular bisector of AC
With A as center, and radius more than half AC,
draw an arc on top and bottom of AC
Now with D as center, and same radius,
draw an arc on top and bottom of AC
3. Mark points where arcs intersect on top and bottom of AC
Join the points.
So, the required line is the perpendicular bisector of AC
Mark point O where perpendicular bisector intersects AC
4. Now, we will mark points D and B
We know that OD = OB = 3.5 cm
Taking 3.5 cm as radius, and O as center,
draw an arc on top and bottom of AC
Where arc intersects perpendicular bisector on top of AC is point D.
And where it intersects perpendicular bisector on bottom of AC is point B
6. Join AB, BC, CD, AD and BD
Label the sides
∴ ABCD is the required rhombus

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.