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

Download PDF of This Page (Size: 323K)

Chart of Quadrilaterals

Chart of Quadrilaterals of various types

Chart of Quadrilaterals

Chart of Quadrilaterals of various types

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

Diagonal BD bisects as well as .

Solution:

ABCD Is Rhombus

ABCD is rhombus AC bisects ∠ A as well as ∠C

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:

  1. ABCD is a square

  2. Diagonal BD bisects ∠B as well as ∠D.

Solution:

ABCD Is a Rectangle

ABCD is a rectangle its diagonal AC also bisects two angles ∠A as well as ∠C

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