Question

prove that the difference between
any two sides of a triangle in lees than it third sides​

Answer 1

Answer:

Step-by-step explanation:

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

Answer 2

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