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

If 2^x = 4^y = 8^z and `1/(2x) + 1/(4y) + 1/(8z) = 4` , find the value of x.

If m = `root(3)(15) and n = root(3)(14), "find the value of " m - n - 1/[ m^2 + mn + n^2 ]`

Evaluate : `4/(216)^(-2/3) + 1/(256)^(-3/4) + 2/(243)^(-1/5)`

If the following pair of the triangle is congruent? state the condition of congruency : 
In  ΔABC and ΔDEF,  ∠B = ∠E = 90^o; AC = DF and BC = EF.

If the following pair of the triangle is congruent? state the condition of congruency: 

In ΔABC and ΔPQR, BC = QR, ∠A = 90°, ∠C = ∠R = 40° and ∠Q = 50°.

On the sides AB and AC of triangle ABC, equilateral triangle ABD and ACE are drawn. Prove that: 

1. ∠CAD = ∠BAE
2. CD = BE

In the following diagram, ABCD is a square and APB is an equilateral triangle.

(i) Prove that: ΔAPD≅ ΔBPC
(ii) Find the angles of ΔDPC.

In the following diagram, AP and BQ are equal and parallel to each other. 

Prove that:  

1. ΔAOP ≅ ΔBOQ.
2. AB and PQ bisect each other.

In the following figure, OA = OC and AB = BC.

Prove that:
(i) ∠AOB = 90o
(ii) ΔAOD ≅ ΔCOD
(iii) AD = CD

In the following figure, OA = OC and AB = BC. 

Prove that: AD = CD

The following figure has shown a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN.
Prove that:  (i) AM = AN  (ii) ΔAMC ≅ ΔANB

The following figure shown a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN.

Prove that:  ΔAMC≅ ΔANB

The following figure has shown a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN.

Prove that: (i) BN = CM (ii) ΔBMC ≅ ΔCNB   

The following figure shown a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN.

Prove that:  

In a triangle, ABC, AB = BC, AD is perpendicular to side BC and CE is perpendicular to side AB. Prove that: AD = CE.

In triangle ABC, AB > AC and D is a point inside BC.
Show that: AB > AD.

Given: ED = EC

Prove: AB + AD > BC.

In an isosceles triangle ABC, sides AB and AC are equal. If point D lies in base BC and point E lies on BC produced (BC being produced through vertex C), prove that:
(i) AC > AD
(ii) AE > AC
(iii) AE > AD

In triangle ABC, side AC is greater than side AB. If the internal bisector of angle A meets the opposite side at point D,
prove that:  ∠ADC is greater than ∠ADB.

In quadrilateral ABCD, side AB is the longest and side DC is the shortest.
Prove that: C > A.