Question

Complete the following statement with reference to the given figure.



(1) l (AP) + l (BP) > _________
(2) l (AP) + l (CP) _______ l (AC)
(3) ________ + l (CP) > l (BC)
(4) l (AB) + ________ > l (BC)

Answer 1

We know that in a triangle, the sum of lengths of any two sides is always greater than the length of the third side.

(1) The sides of ∆ABP are AB, BP and AP.
Using the above stated property,
l (AP) + l (BP) > l (AB)

(2) The sides of ∆ACP are AC, CP and AP.
Using the above stated property,
l (AP) + l (CP) > l (AC)

(3) The sides of ∆BPC are BP, PC and BC.
Using the above stated property,
l (BP) + l (CP) > l (BC)

(4) The sides of ∆ABC are AB, BC and AC.
Using the above stated property,
l (AB) + l (AC) > l (BC)