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

In a triangle ABC, if the bisectors of angles ABC and ACB meet at M then prove that: ∠BMC = 90° + `(1)/(2)` ∠A.

If bisectors of angles A and D of a quadrilateral ABCD meet at 0, then show that ∠B + ∠C = 2 ∠AOD

If each angle of a triangle is less than the sum of the other two angles of it; prove that the triangle is acute-angled.

If the angles of a triangle are in the ratio 2: 4: 6; show that the triangle is a right-angled triangle.

In a triangle, the sum of two angles is 139° and their difference is 5°; find each angle of the triangle.

In a right-angled triangle ABC, ∠B = 90°. If BA and BC produced to the points P and Q respectively, find the value of ∠PAC + ∠QCA.

Construct a trapezium ABCD in which
AB = 3.5cm, BC = 6cm, CD = 3.5cm, AD = 4.4cm and AD || BC.

Construct a trapezium ABCD in which
AB = 4.6cm, BC = 6.4cm, CD = 5.6cm, ∠B = 60° and AD || BC.

Find the area of an isosceles triangle ABC in which AB = AC = 6 cm, ∠A = 90°. Also, find the length of perpendicular from A to BC.

Find the area of an equilateral triangle of side 20 cm.

Find the perimeter of an equilateral triangle whose area is `16sqrt(3)"cm"`.

Find the area of an equilateral triangle having perimeter of 18cm.

Find the area of the shaded region in the figure as shown, in which DPQS is an equilateral triangle and ∠PQR = 90°.

The area of an equilateral triangle is numerically equal to its perimeter. Find the length of its sides, correct two decimal places.

In a right-angled triangle PQR right-angled at Q, QR = x cm, PQ = (x + 7) cm and area = 30 cm². Find the sides of the triangle.

In a right-angled triangle ABC, if ∠B = 90°, AB - BC = 2 cm; AC - BC = 4 and its perimeter is 24 cm, find the area of the triangle.

In a right-angled triangle ABC, if ∠B = 90°, AB - BC = 2 cm; AC - BC = 4 and its perimeter is 24 cm, find the area of the triangle.

Find the area of an isosceles triangle whose perimeter is 50cm and the base is 24cm.

Find the area of an isosceles triangle whose perimeter is 72cm and the base is 20cm.

Find the base of an isosceles triangle whose area is 192cm² and the length of one of the equal sides is 20cm.