English Medium कक्षा ९ - CBSE Question Bank Solutions

Two lines AB and CD intersect at O such that BC is equal and parallel to AD. Prove that the lines AB and CD bisect at O. 

BD and CE are bisectors of ∠B and ∠C of an isosceles ΔABC with AB = AC. Prove that BD = CE. 

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

In an isosceles triangle, if the vertex angle is twice the sum of the base angles, calculate the angles of the triangle. 

PQR is a triangle in which PQ = PR and S is any point on the side PQ. Through S, a line is drawn parallel to QR and intersecting PR at T. Prove that PS = PT.  

In a ΔABC, it is given that AB = AC and the bisectors of ∠B and ∠C intersect at O. If M is a point on BO produced, prove that ∠MOC = ∠ABC. 

P is a point on the bisector of an angle ∠ABC. If the line through P parallel to AB meets BC at Q, prove that triangle BPQ is isosceles.  

Prove that each angle of an equilateral triangle is 60°. 

Angles A, B, C of a triangle ABC are equal to each other. Prove that ΔABC is equilateral. 

ABC is a triangle in which ∠B = 2 ∠C. D is a point on BC such that AD bisects ∠BAC and AB = CD.
Prove that ∠BAC = 72°. 

ABC is a right angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C. 

In a ΔPQR, if PQ = QR and L, M and N are the mid-points of the sides PQ, QR and RP
respectively. Prove that LN = MN. 

ABC is a triangle and D is the mid-point of BC. The perpendiculars from D to AB and AC are equal. Prove that the triangle is isosceles. 

ABC is a triangle in which BE and CF are, respectively, the perpendiculars to the sides AC and AB. If BE = CF, prove that ΔABC is isosceles  

Which of the following statements are true (T) and which are false (F): 

Sides opposite to equal angles of a triangle may be unequal 

Which of the following statements are true (T) and which are false (F): 

Angles opposite to equal sides of a triangle are equal 

Which of the following statements are true (T) and which are false (F): 

The measure of each angle of an equilateral triangle is 60° 

Which of the following statements are true (T) and which are false (F) : 

If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles.  

Which of the following statements are true (T) and which are false (F): 

The bisectors of two equal angles of a triangle are equal 

Which of the following statements are true (T) and which are false (F):  

If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles.