English Medium Class 9 - CBSE Question Bank Solutions

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. 

Factorize the following expressions:

x3 + 6x² +12x +16

Factorize the following expressions:

a³ + b³ + a + b

Factorize the following expressions:

`a^3 - 1/a^3 - 2a + 2/a`

If the bisector of the exterior vertical angle of a triangle be parallel to the base. Show that the triangle is isosce

Factorize the following expressions:

a³ + 3a²b + 3ab² + b³ - 8

Factorize the following expressions:

8a³ - b³ - 4ax + 2bx

Simplify `(173 xx 173 xx 173 xx 127 xx 127 xx 127)/(173 xx 173 xx 173 xx 127 xx 127 xx 127)`

Simplify `(155 xx 155 xx 155 - 55 xx 55 xx 55)/(155 xx 155 + 155 xx 55 + 55 xx 55)`

Factorize 64a³ +125b³ + 240a²b + 300ab²

Factorize 125x³ - 27 y³ - 225x² y +135xy²