# NCERT Class 9 Solutions: Quadrilaterals (Chapter 8) Exercise 8.1 – Part 4

Get unlimited access to the best preparation resource for NSTSE : fully solved questions with step-by-step explanation- practice your way to success.

Download PDF of This Page (Size: 176K) ↧

Chart of Quadrilaterals

Q-7 ABCD is a rhombus. Show that diagonal bisects as well as and

Diagonal BD bisects as well as.

Solution:

Given,

ABCD is a rhombus

AC and BD are its diagonals.

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,

(Sides of a rhombus are equal)

…….equation (3) (Angles opposite of equal sides of a triangle are equal.)

Also, and so …..equation (4) (Alternate interior angles)

From Equation (3) and (4)

Therefore, AC bisects.

Similarly, diagonal BD bisects as well as.

Q-8 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:

Given ABCD is a rectangle, AC is bisects, as well as

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