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

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.

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

In the following figure; AB is the largest side and BC is the smallest side of triangle ABC.
Write the angles x^o, y^o and z^o in ascending order of their values.

In the following diagram; AD = AB and AE bisect angle A.

Prove that:
(i) BE = DE
(ii) ∠ABD > ∠C

P is any point inside the triangle ABC.
Prove that: ∠BPC > ∠BAC.

In the following figure, ABC is an equilateral triangle and P is any point in AC;
prove that: BP > PC

In a quadrilateral ABCD; prove that:
(i) AB+ BC + CD > DA
(ii) AB + BC + CD + DA > 2AC
(iii) AB + BC + CD + DA > 2BD

Using ruler and compasses only, construct a rectangle each of whose diagonals measure 6 cm and the diagonals interest at an angle of 45^o.

Construct a rectangle ABCD, when:
Its sides are 6.0 cm and 7.2 cm.

Construct a rectangle ABCD, when:
One side = 4 cm and one diagonal is 5 cm. Measure the length of the other side.

Construct a rectangle ABCD, when:
One diagonal = 6.0 cm and the acute angle between the diagonals = 45^o.

Construct a rectangle ABCD, when:
Area = 24 cm² and base = 4.8 cm².

Construct a rectangle ABCD, when:
Area = 36 cm² and height = 4.5 cm.

The diagonal of a rectangular plot is 34 m and its perimeter is 92 m. Find its area.