English Medium कक्षा ९ - CBSE Question Bank Solutions for Mathematics

If one angle of a triangle is equal to the sum of the other two, show that the triangle is a
right triangle. 

Factorize the following expressions:

(a + b)³ – 8(a – b)³

Factorize the following expressions: 

( x + 2)³ + ( x - 2)³

Factorize the following expressions:

`8x^2y^3 - x^5`

Factorize the following expressions:

1029 – 3x³

ABC is a triangle in which ∠A — 72°, the internal bisectors of angles B and C meet in O.
Find the magnitude of ∠BOC.

Factorize the following expressions:

x⁶ + y⁶

Factorize the following expressions:

x³y³ + 1

The bisectors of base angles of a triangle cannot enclose a right angle in any case. 

Factorize the following expressions:

x⁴y⁴ - xy

If the bisectors of the base angles of a triangle enclose an angle of 135°, prove that the triangle is a right triangle.  

In a ΔABC, ∠ABC = ∠ACB and the bisectors of ∠ABC and ∠ACB intersect at O such that ∠BOC = 120°. Show that ∠A = ∠B = ∠C = 60°. 

Can a triangle have two right angles? Justify your answer in case.

Can a triangle have two obtuse angles?  Justify your answer in  case.

Can a triangle have two acute angles?Justify your answer in case. 

Factorize the following expressions: 

a¹² + b¹²

Can a triangle have  All angles more than 60°? Justify your answer in case.

Can a triangle have All angles less than 60° Justify your answer in case.

Can a triangle have All angles equal to 60°? Justify your answer in case.

If each angle of a triangle is less than the sum of the other two, show that the triangle is acute angled.