Question

Prove that the difference of two sides is less than the third side

Answer 1

Answer:

Start with the Triangle Inequality Theorem which is, the sum of any two sides of a triangle must be greater than the third. if the difference of any two sides of a triangle is not less than its third side, it does not obey the rule… Clearly the sum of the lengths of any 2 sides must be larger than the remaining side.

explanation:

Answer 2

TO PROVE THAT: AC - AB < BC

CONSTRUCTION: From the longer side AC, cut a segment AD = AB

So, now, we need to prove that AC - AD < BC

=>TO PROVE first: that DC < BC

PROOF:< ABD = < ADB = a ( by construction)

< DBC = p, & < BDC = k

Since, k = a + A ( exterior < of a triangle) ……. (1)

p = a - C ( again by exterior < of a triangle) ….(2)

By comparing (1) & (2)

(a + A) > (a - C) , as all these angle variables >0

=> k > p

=> side opposite to k > side opposite to p

=> BC > DC

=> DC < BC

=> AC - AD < BC

=> AC - AB < BC

[ hence proved]