Example 2
Show that the diagonals of a rhombus are perpendicular to each other.
Given: Rhombus ABCD
To prove : AC BD
Proof:
Since ABCD is a rhombus
AB = BC = CD = DA
In AOB and COB,
OA = OC
OB = OB
AB = CB
AOB COB
AOB = COB
Since AC is a line,
AOB + COB = 180
AOB + AOB = 180
2 AOB = 180
AOB = 180" " /2 = 90
From (1)
COB = AOB
COB = 90
Also,
DOC = AOB = 90
AOD = COB = 90
Since DOC = AOB = AOD = COB = 90
AC BD
The diagonals of a rhombus are perpendicular to each other.

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.