Frank solutions for Mathematics [English] Class 9 ICSE chapter 13 - Inequalities in Triangles [Latest edition]

Name the greatest and the smallest sides in the following triangles:
ΔABC, ∠ = 56°, ∠B = 64° and ∠C = 60°.

Name the greatest and the smallest sides in the following triangles:
ΔDEF, ∠D = 32°, ∠E = 56° and ∠F = 92°.

Name the greatest and the smallest sides in the following triangles:
ΔXYZ, ∠X = 76°, ∠Y = 84°.

Arrange the sides of the following triangles in an ascending order:
ΔABC, ∠A = 45°, ∠B = 65°.

Arrange the sides of the following triangles in an ascending order:
ΔDEF, ∠D = 38°, ∠E = 58°.

Name the smallest angle in each of these triangles:
In ΔABC, AB = 6.2cm, BC = 5.6cm and AC = 4.2cm

Name the smallest angle in each of these triangles:
In ΔPQR, PQ = 8.3cm, QR = 5.4cm and PR = 7.2cm

Name the smallest angle in each of these triangles:
In ΔXYZ, XY = 6.2cm, XY = 6.8cm and YZ = 5cm

In a triangle ABC, BC = AC and ∠ A = 35°. Which is the smallest side of the triangle?

In ΔABC, the exterior ∠PBC > exterior ∠QCB. Prove that AB > AC.

ΔABC is isosceles with AB = AC. If BC is extended to D, then prove that AD > AB.

Prove that the perimeter of a triangle is greater than the sum of its three medians.

Prove that the hypotenuse is the longest side in a right-angled triangle.

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.