NCERT Class 9 Solutions: Quadrilaterals (Chapter 8) Exercise 8.1 – Part 4
Chart of Quadrilaterals
Q7 ABCD is a rhombus. Show that diagonal bisects as well as and
Diagonal BD bisects as well as.
Solution:
Given,
Proof,

(Sides of a rhombus are equal)

………..equation (1) (Angles opposite of equal sides of a triangle are equal.)


Also, , therefore, ……..equation (2) (Alternate interior angles)
From equation (1) and (2),
Therefore, AC bisects.
Similarly,
Also, and so …..equation (4) (Alternate interior angles)
From Equation (3) and (4)
Therefore, AC bisects.
Similarly, diagonal BD bisects as well as.
Q8 ABCD is a rectangle in which diagonal bisects as well as. Show that:

ABCD is a square

Diagonal BD bisects ∠B as well as ∠D.
Solution:
Solution (i):

(AC bisects as well as )

(Sides opposite to equal angles of a triangle are equal)

Also, (Opposite sides of a rectangle)

Therefore,

Thus, ABCD is a square.
Solution (ii):


(Angles opposite to equal sides are equal)

Also, (Alternate interior angles) therefore,

Thus, BD bisects

Now,
Thus, BD bisects