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

In quadrilateral ABCD, AD = BC and BD = CA.
Prove that:
(i) ∠ADB = ∠BCA
(ii) ∠DAB = ∠CBA

A point O is taken inside a rhombus ABCD such that its distance from the vertices B and D are equal. Show that AOC is a straight line.

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

Prove that: ΔAOD≅ ΔCOD

In the following figure, AB = EF, BC = DE and ∠B = ∠E = 90°.

Prove that AD = FC.

AD and BC are equal perpendiculars to a line segment AB. If AD and BC are on different sides of AB prove that CD bisects AB.

In ΔABC, AB = AC and the bisectors of angles B and C intersect at point O.
Prove that : (i) BO = CO
                   (ii) AO bisects angle BAC.

In the following figure, ∠A = ∠C and AB = BC.
Prove that ΔABD ≅ ΔCBE. 

In the following figure, ABC is an equilateral triangle in which QP is parallel to AC. Side AC is produced up to point R so that CR = BP.

Prove that QR bisects PC.
Hint: ( Show that ∆ QBP is equilateral
⇒ BP = PQ, but BP = CR
⇒ PQ = CR ⇒ ∆ QPM ≅ ∆ RCM ).

PQRS is a parallelogram. L and M are points on PQ and SR respectively such that PL = MR.
Show that LM and QS bisect each other.

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

Prove that: AD = CE.

Construct a rhombus, having given one side = 4.8 cm and one angle = 75^o.

Construct a rhombus ABCD, when:
Its one side = 6 cm and ∠A = 60^o.

Construct a rhombus ABCD, when:
One side = 5.4 cm and one diagonal is 7.0 cm.

Construct a rhombus ABCD, when:
Diagonal AC = 6.3 cm and diagonal BD = 5.8 cm.

Construct a rhombus ABCD, when:
One side = 5.0 cm and height = 2.6 cm.

Construct a rhombus ABCD, when: Diagonal AC = 6.0 cm and height = 3.5 cm.

Construct a rhombus ABCD, when: A = 60° and height = 3.0 cm.

The value of π up to 50 decimal place is
3.14159265358979323846264338327950288419716939937510
(i) Make a frequency distribution table of digits from 0 to 9 after the decimal place.
(ii) Which are the most and least occurring digits?

Fill in the blank in the following table:

Given below are the marks obtained by 30 students in an examination:

Taking class intervals 1-10, 11-20, ....., 41-50; make a frequency table for the above distribution.