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

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).

In the figure of question 2, if E is the mid-point of median AD, then

prove that:

Area (ΔABE) = `1/4` Area (ΔABC).

The base BC of triangle ABC is divided at D so that BD = `1/2`DC.
Prove that area of ΔABD = `1/3` of the area of ΔABC.

In the following figure, OAB is a triangle and AB || DC.

If the area of ∆ CAD = 140 cm² and the area of ∆ ODC = 172 cm²,
find : (i) the area of ∆ DBC
(ii) the area of ∆ OAC
(iii) the area of ∆ ODB.

Use the table given below to find:
(a) The actual class limits of the fourth class.
(b) The class boundaries of the sixth class.
(c) The class mark of the third class.
(d) The upper and lower limits of the fifth class.
(e) The size of the third class.

The base of an isosceles triangle is 24 cm and its area is 192 sq. cm. Find its perimeter.

Four identical cubes are joined end to end to form a cuboid. If the total surface area of the resulting cuboid as 648 m²; find the length of the edge of each cube. Also, find the ratio between the surface area of the resulting cuboid and the surface area of a cube.

The volume of a cube is 729 cm³. Find its total surface area.