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Let CA and CB be two lines drawn from the point C to the extremities of the straight line AB. Let OA and OB be two lines similarly drawn, but included by CA and CB.To prove
Let CA and CB be two lines drawn from the point C to the extremities of the straight line AB. Let OA and OB be two lines similarly drawn, but included by CA and CB.To prove
Prove CA+CB > OA+OB.
Prove CA+CB > OA+OB.
Proof.
Proof.
Produce AO to meet the line CB at E. Then
CA + CE > OA + OE (shortest distance between 2 points is a straight line)
BE + OE > OB
Add these inequalities,
CA + CE + BE + OE > OA + OE + OB
CA + CB + OE > OA + OE + OB (CE + BE equal CB)
CA + CB > OA + OB (subtract OE from both sides)
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