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

E is the mid-point of side AB and F is the mid-point of side DC of parallelogram ABCD. Prove that AEFD is a parallelogram.

The diagonal BD of a parallelogram ABCD bisects angles B and D. Prove that ABCD is a rhombus.

The alongside figure shows a parallelogram ABCD in which AE = EF = FC.

Prove that:

1. DE is parallel to FB
2. DE = FB
3. DEBF is a parallelogram.

In the alongside diagram, ABCD is a parallelogram in which AP bisects angle A and BQ bisects angle B.

Prove that: 

1. AQ = BP
2. PQ = CD
3. ABPQ is a parallelogram.

In the given figure, ABCD is a parallelogram.

Prove that: AB = 2 BC.

Prove that the bisectors of opposite angles of a parallelogram are parallel.

The following figure shows a trapezium ABCD in which AB is parallel to DC and AD = BC.

Prove that:
(i) ∠DAB = ∠CBA
(ii) ∠ADC = ∠BCD
(iii) AC = BD
(iv) OA = OB and OC = OD.

In parallelogram ABCD, the bisector of angle A meets DC at P and AB = 2 AD.
Prove that:
(i) BP bisects angle B.
(ii) Angle APB = 90^o.

Points M and N are taken on the diagonal AC of a parallelogram ABCD such that AM = CN. Prove that BMDN is a parallelogram.

Construct a square ABCD, when: One side = 4.5 cm.

Construct a square ABCD, when: One diagonal = 5.4 cm.

Construct a square ABCD, when: Perimeter = 24 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.

Construct the frequency distribution table from the following cumulative frequency table:

(i) State the number of students in the age group 10 - 13.
(ii) State the age-group which has the least number of students.

Construct a frequency table from the following data:

Construct a frequency distribution table from the following cumulative frequency distribution:

Construct a cumulative frequency distribution table from the frequency table given below:
( i )

( ii )

Construct a cumulative frequency distribution table from the frequency table given below: