English Medium Class 9 - CBSE Question Bank Solutions for Mathematics

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.

In Fig. 10.23, PQRS is a square and SRT is an equilateral triangle. Prove that
(i) PT = QT (ii) ∠TQR = 15° 

Prove that the medians of an equilateral triangle are equal. 

In a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C. 

In a ΔABC, if AB = AC and ∠B = 70°, find ∠A. 

The vertical angle of an isosceles triangle is 100°. Find its base angles. 

In Figure 10.24, AB = AC and ∠ACD =105°, find ∠BAC. 

Find the measure of each exterior angle of an equilateral triangle. 

If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other. 

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.