(English Medium) ICSE Class 9 - CISCE Question Bank Solutions

In the figure, given below, AB = AC.

Prove that: ∠BOC = ∠ACD.

Calculate x :

Calculate x :

In the given figure; AB = BC and AD = EC.
Prove that: BD = BE.

Prove that a triangle ABC is isosceles, if: altitude AD bisects angles BAC.

Prove that a triangle ABC is isosceles, if: bisector of angle BAC is perpendicular to base BC.

In the given figure, AD = AB = AC, BD is parallel to CA and angle ACB = 65°. Find angle DAC.

In triangle ABC; AB = AC and ∠A : ∠B = 8 : 5; find angle A.

Using the information given of the following figure, find the values of a and b.

If the equal sides of an isosceles triangle are produced, prove that the exterior angles so formed are obtuse and equal.

In isosceles triangle ABC, AB = AC. The side BA is produced to D such that BA = AD.
Prove that: ∠BCD = 90°

ABC is a triangle. The bisector of the angle BCA meets AB in X. A point Y lies on CX such that AX = AY.
Prove that: ∠CAY = ∠ABC.

Use the given figure to prove that, AB = AC.

Prove that the medians corresponding to equal sides of an isosceles triangle are equal.

The bisectors of the equal angles B and C of an isosceles triangle ABC meet at O. Prove that AO bisects angle A.

Using ruler and compasses only, construct a trapezium ABCD, in which the parallel sides AB and DC are 3.3 cm apart; AB = 4.5 cm, angle A = 120^o BC = 3.6 cm and angle B is obtuse.

Construct a trapezium ABCD, when:
AB = 4.8 cm, BC = 6.8 cm, CD = 5.4 cm, angle B = 60^o and AD // BC.

Construct a trapezium ABCD, when:

AB = CD = 3.2 cm, BC = 6.0 cm, AD = 4.4 cm and AD // BC.

The following figure shows a triangle ABC in which P, Q, and R are mid-points of sides AB, BC and CA respectively. S is mid-point of PQ:
Prove that: ar. ( ∆ ABC ) = 8 × ar. ( ∆ QSB )

In the given figure; AD is median of ΔABC and E is any point on median AD.
Prove that Area (ΔABE) = Area (ΔACE).