Draw five triangles and measure their sides. Check in each case, if the sum of the lengths of any two sides is always greater than the third side.

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Infinity Learn · Accepted Answer

Case I. In ∆ABCConsider AB $$=$$ $$2.5$$ cm, BC $$=$$ $$4.8$$ cm and AC $$=$$ $$5.2$$ cmAB $$+$$ BC $$=$$ $$2.5$$ cm $$+$$ $$4.8$$ cm $$=$$ $$7.3$$ cmSince, $$7.3$$ > $$5.2$$ , AB $$+$$ BC > ACTherefore, the sum of any two sides of a triangle is greater than the third side.Case II. In ∆PQR,Consider PQ $$=$$ $$2$$ cm, QR $$=$$ $$2.5$$ cm and PR $$=$$ $$3.5$$ cmPQ $$+$$ QR $$=$$ $$2$$ cm $$+$$ $$2.5$$ cm $$=$$ $$4.5$$ cmSince, $$4.5$$ > $$3.5$$, PQ $$+$$ QR > PRTherefore, the sum of any two sides of a triangle is greater than the third side.Case III. In ∆XYZ,Consider XY $$=$$ $$5$$ cm, YZ $$=$$ $$3$$ cm and ZX $$=$$ $$6.8$$ cmXY $$+$$ YZ $$=$$ $$5$$ cm $$+$$ $$3$$ cm $$=$$ $$8$$ cmSince, $$8$$ > $$6.8$$, XY $$+$$ YZ > ZXTherefore, the sum of any two sides of a triangle is greater than the third side.Case IV. In ∆MNS,Consider MN $$=$$ $$2.7$$ cm, NS $$=$$ $$4$$ cm and MS $$=$$ $$4.7$$ cmMN $$+$$ NS $$=$$ $$2.7$$ cm $$+$$ $$4$$ cm $$=$$ $$6.7$$ cmSince, $$6.7$$ >$$4.7$$, MN $$+$$ NS > MSHence, the sum of any two sides of a triangle is greater than the third side.Case V. In ∆KLM,Consider KL $$=$$ $$3.5$$ cm, LM $$=$$ $$3.5$$ cm and KM $$=$$ $$3.5$$ cmKL $$+$$ LM $$=$$ $$3.5$$ cm $$+$$ $$3.5$$ cm $$=$$ $$7$$ $$cm7$$ cm > $$3.5$$ cm, KL $$+$$ LM > KMTherefore, the sum of any two sides of a triangle is always greater than the third side.

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