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

D is a point on the side of the BC of ΔABC. Prove that the perimeter of ΔABC is greater than twice of AD.

For any quadrilateral, prove that its perimeter is greater than the sum of its diagonals.

ABCD is a quadrilateral in which the diagonals AC and BD intersect at O. Prove that AB + BC + CD + AD < 2(AC + BC).

In ABC, P, Q and R are points on AB, BC and AC respectively. Prove that AB + BC + AC > PQ + QR  + PR.

In ΔPQR, PR > PQ and T is a point on PR such that PT = PQ. Prove that QR > TR.

ABCD is a trapezium. Prove that:

CD + DA + AB + BC > 2AC.

ABCD is a trapezium. Prove that:

CD + DA + AB > BC.

In the given figure, ∠QPR = 50° and ∠PQR = 60°. Show that : PN < RN

In the given figure, ∠QPR = 50° and ∠PQR = 60°. Show that: SN < SR

In ΔABC, BC produced to D, such that, AC = CD; ∠BAD = 125° and ∠ACD = 105°. Show that BC > CD.

In ΔPQR, PS ⊥ QR ; prove that: PQ > QS and PQ > PS

In ΔPQR, PS ⊥ QR ; prove that: PQ > QS and PR > PS

In ΔPQR, PS ⊥ QR ; prove that: PQ + PR > QR and PQ + QR >2PS.

In the given figure, T is a point on the side PR of an equilateral triangle PQR. Show that PT < QT

In the given figure, T is a point on the side PR of an equilateral triangle PQR. Show that RT < QT

In ΔPQR is a triangle and S is any point in its interior. Prove that SQ + SR < PQ + PR.

Prove that in an isosceles triangle any of its equal sides is greater than the straight line joining the vertex to any point on the base of the triangle.

ΔABC in a isosceles triangle with AB = AC. D is a point on BC produced. ED intersects AB at E and AC at F. Prove that AF > AE.

In ΔABC, AE is the bisector of ∠BAC. D is a point on AC such that AB = AD. Prove that BE = DE and ∠ABD > ∠C.

In ΔABC, D is a point in the interior of the triangle. Prove that DB + DC < AB + AC.