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