Ex 8.1, 8
ABCD is a rectangle in which diagonal AC bisects A as well as C. Show that:
ABCD is a square
Given:
Rectangle ABCD where
AC bisects A, i.e. 1 = 2
& AC bisects C, i.e. 3 = 4
To prove: ABCD is a square
Proof: A square is a rectangle when all sides are equal
Now,
AD BC
& AC as transversal
1 = 4
Now,
1 = 2
& 1 = 4
Hence,
2 = 4
In ABC,
2 = 4
So, BC = AB
But BC = AD & AB = DC
From (1) & (2)
AB = BC = CD = DA
So, ABCD is a rectangle with all sides equal
Hence, ABCD is a square.
Ex 8.1, 8
ABCD is a rectangle in which diagonal AC bisects A as well as C. Show that:
(ii) diagonal BD bisects B as well as D.
In previous part we proved,
ABCD is a square
And diagonals of a square bisects its angles
So, Diagonal BD bisects B & D.
Hence proved

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.

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