## 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, PS QR ; prove that:
PQ > QS and PQ > PS Solution 9 Question 10
In PQR, PS QR ; prove that:
PR > PS Solution 10 Question 11
In PQR, PS QR ; 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 