Ex 8.1, 2
If the diagonals of a parallelogram are equal, then show that it is a rectangle.
Given: Let ABCD be a parallelogram
where AC = BD
To prove: ABCD is a rectangle
Proof: Rectangle is a parallelogram with one angle 90
We prove that one of its interior angles is 90 .
In ABC and DCB,
AB = DC
BC = BC
AC = DB
ABC DCB
ABC = DCB
Now,
AB DC
& BC is a transversal
B + C= 180
B + B = 180
2 B = 180
B = "180 " /"2" = 90
So, ABCD is a parallelogram with one angle 90
ABCD is a rectangle

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

Hi, it looks like you're using AdBlock :(

Displaying ads are our only source of revenue. To help Teachoo create more content, and view the ad-free version of Teachooo... please purchase Teachoo Black subscription.

Please login to view more pages. It's free :)

Teachoo gives you a better experience when you're logged in. Please login :)

Solve all your doubts with Teachoo Black!

Teachoo answers all your questions if you are a Black user!