Question 1
Question: ABC is a triangle in which AB=AC. D is a point on BC produced. Prove that AD>AB.
Answer: Given:
AB=AC
D is a point on BC produced.
To prove:
AD>AB
Proof
AB=AC (given)
Question 2
Question: In the adjoining diagram, name the shortest and the longest side. B is the greatest angle.
Answer: 
Angle A is the least angle.
Question 3
Question: 
Answer: 
(
exterior angle = sum of int. opposite angle)
Question 4
Question: 
Answer: To prove:
Proof:
Combining relation (i) and (ii), we can write
Question 5
Question: 
Answer: Solution:
Question 6
Question: 
Answer: Data:
In quadrilateral ABCD, AD is the largest side and BC is the shortest side.
To prove:
Construction:
Join BD and AC.
Proof:
In D ABD, AD > AB ( given)
DC > BC
i.e., ABC (or B) > ADC (or D)
In D ADC,
AD>DC (given)
AB>BC ( given)
Question 7
Question: 
Answer: Given:
To prove:
Proof:
(corollary on theorem on
exterior angle of a triangle)
Question 8
Question: ABCD is a quadrilateral in which AB=BC, AD=DC and AD>AB. 
Answer: Given:
In the quadrilateral ABCD, AB=BC, AD=DC and AD>AB
To prove:
Construction:
Join BD.
Proof:
In D ABD, AD>AB ( given)
CD > BC
S since CD=AD and BC=AB and AD>AB
By adding (i) and (ii), we get
Question 9
Question: In the adjoining figure, AGH is an isosceles triangle with base GH. Prove that KH>KG.
Answer: Given:
In D AGH, AG=AH
To prove:
KH > KG
Proof:
In D AGH,
AG=AH ( given)
Question 10
Question: In the adjoining figure, LM is the base of isosceles D KLM. Prove that KM>XL.
Answer: Given:
In D KLM ,
KL=KM
To prove:
KM > XL
Proof:
KL > XL
(theorem on inequality KLM is an isosceles triangle)
But KL = KM
\ KM > XL
