FRANK Solutions for Class 9 Maths Chapter 13 - Inequalities in Triangles
How to show that the perimeter of a given triangle is more than the sum of its medians? Find answers in TopperLearning’s Frank solutions for ICSE Class 9 Mathematics Chapter 13 Inequalities in Triangles. Revise the application of properties of triangles to provide proofs in answers such as a particular side of an isosceles triangle is greater than another side.
Revise the Exterior Angle property, Angle Sum property and carious other properties of the triangle with our Frank textbook solutions. Practice makes you perfect; and that is why ICSE Class 9 Maths videos, online practice tests, and more study aids are at available on TopperLearning.
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Chapter 13 - Inequalities in Triangles Exercise Ex. 13.1
Question 1(a)
Name the greatest and the smallest sides in the following triangles:
ABC, ∠ = 56o, ∠B = 64o and ∠C = 60o.
Solution 1(a)
Question 1(b)
Name the greatest and the smallest sides in the following triangles:
DEF, ∠D
= 32o, ∠E = 56o and ∠F
= 92o.
Solution 1(b)
Question 1(c)
Name the greatest and the smallest sides in the following triangles:
XYZ, ∠X
= 76o, ∠Y = 84o.
Solution 1(c)
Question 2(a)
Arrange the sides of the following triangles in an ascending order:
ABC, ∠A
= 45o, ∠B = 65o.
Solution 2(a)
Question 2(b)
Arrange the sides of the following triangles in an ascending order:
DEF, ∠D
= 38o, ∠E = 58o.
Solution 2(b)
Question 3
Solution 3
Question 4
In a triangle ABC, BC = AC and ∠ A = 35°. Which is the smallest side of the triangle?
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Question 8
Solution 8
Question 9
Solution 9
Question 10
Solution 10
Question 11
Solution 11
Question 12
Solution 12
Question 13
Solution 13
Question 14
Solution 14
Question 15
n the given figure, ∠QPR = 50o and ∠PQR = 60o. Show that :
a. PN < RN
b. SN < SR
Solution 15
Question 16
In ABC, BC produced to D, such that, AC = CD; ∠BAD
= 125o and ∠ACD = 105o.
Show that BC > CD.
Solution 16
Question 17(a)
In PQR, PS
QR ; prove that:
PQ > QS and PQ > PS
Solution 17(a)
Question 17(b)
In
PQR, PS
QR ; prove that:
PR > PS
Solution 17(b)
Question 17(c)
In
PQR, PSQR ; prove that:
PQ + PR > QR and PQ + QR >2PS.
Solution 17(c)
Question 18
In the given figure, T is a point on the side PR of triangle PQR. Show that
a. PT < QT
b. RT < QT
Solution 18
Question 19
In
PQR is a triangle and S is any point in its interior. Prove
that SQ + SR < PQ + PR.
Solution 19
Question 20
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.
Solution 20
Question 21
ABC 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.
Solution 21
Question 22
In
ABC, AE is the bisector of ∠BAC.
D is a point on AC such that AB = AD. Prove that BE = DE and ∠ABD
> ∠C.
Solution 22
Question 23
In
ABC, D is a point in the interior of the triangle. Prove
that DB + DC < AB + AC.
Solution 23
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