## Chapter 13 - Inequalities in Triangles Exercise Ex. 13.1

Question 1
Name the greatest and the smallest sides in the following triangles:
ABC, = 56o, B = 64o and C = 60o.
Solution 1

Question 2
Name the greatest and the smallest sides in the following triangles:
DEF, D = 32o, E = 56o and F = 92o.
Solution 2
Question 3
Name the greatest and the smallest sides in the following triangles:
XYZ, X = 76o, Y = 84o.
Solution 3

Question 4
Arrange the sides of the following triangles in an ascending order:
ABC, A = 45o, B = 65o.
Solution 4
Question 5
Arrange the sides of the following triangles in an ascending order:
DEF, D = 38o, E = 58o.
Solution 5
Question 6
In a triangle ABC, BC = AC and A = 35°. Which is the smallest side of the triangle?
Solution 6

Question 7
n the given figure, QPR = 50o and PQR = 60o. Show that :
a. PN < RN
b. SN < SR

Solution 7

Question 8
In ABC, BC produced to D, such that, AC = CD; BAD = 125o and ACD = 105o. Show that BC > CD.
Solution 8

Question 9
In PQR, PSQR ; prove that:
PQ > QS and PQ > PS
Solution 9

Question 10
In PQR, PSQR ; prove that:
PR > PS
Solution 10

Question 11
In PQR, PSQR ; prove that:
PQ + PR > QR and PQ + QR >2PS.
Solution 11

Question 12
In the given figure, T is a point on the side PR of triangle PQR. Show that
a. PT < QT
b. RT < QT
Solution 12

Question 13
In PQR is a triangle and S is any point in its interior. Prove that SQ + SR < PQ + PR.
Solution 13

Question 14
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 14

Question 15
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 15

Question 16
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 16

Question 17
In ABC, D is a point in the interior of the triangle. Prove that DB + DC < AB + AC.
Solution 17

Question 18
Solution 18
Question 19
Solution 19
Question 20
Solution 20
Question 21
Solution 21
Question 22
Solution 22
Question 23
Solution 23
Question 24
Solution 24
Question 25
Solution 25
Question 26
Solution 26
Question 27
Solution 27
Question 28
Solution 28