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

In a triangle PQR, ∠P + ∠Q = 130° and ∠P + ∠R = 120°. Calculate each angle of the triangle.

The angles of a triangle are (x + 10)°, (x + 30)° and (x - 10)°. Find the value of 'x'. Also, find the measure of each angle of the triangle.

Use the given figure to find the value of y in terms of p, q and r.

In the figure given below, if RS is parallel to PQ, then find the value of ∠y.

In a triangle PQR, the internal bisectors of angles Q and R meet at A and the external bisectors of the angles Q and R meet at B. Prove that: ∠QAR + ∠QBR = 180°.

Use the given figure to show that: ∠p + ∠q + ∠r = 360°.

In a triangle ABC. If D is a point on BC such that ∠CAD = ∠B, then prove that: ∠ADC = ∠BAC.

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°.