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

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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