...is greater than the third side. Help. — Apply Postulate 4. Corollary. — The difference between any two sides of a triangle is less than the third side. Help. — Apply Axiom 3 to the conclusion of Theorem I. 119. Theorem II. — The sum of the angles...

...306. If from any point E in A AB C EB and EC are drawn, then UNEQUAL LINES AND UNEQUAL ANGLES Ex. 307. The difference of any two sides of a triangle is less than the third side. Ex. 308. A diagonal of a quadrilateral is less than one half the perimeter of the figure. PROPOSITION...

...AABC, EB and EC are drawn, then AB + AC > EB + EC. HINT. Produce BE until it meets AC in D. Ex. 6. The difference of any two sides of a triangle is less than the third side. PROPOSITION XXX. THEOREM 129. // two sides of a triangle are unequal, the angles opposite are unequal,...

...=> AB + BC > AB + DC [Given : AB = AD] => BC > DC Or CD < BC Hence Proved. Example 18 : Prove that the difference of any two sides of a triangle is less than the third side. Solution : Let the given triangle be A ABC which has AB > AC. So, required to prove is : AB - AC <...

...bisector of ZA, and applying i. 17 to the two triangles thus formed. tEx. 643. The difference between any two sides of a triangle is less than the third side. Prove this (i) by means of the same construction as in fig. 136. (ii) by means of the result of i....

...BA > BD, CA > CD. (b) If AB > AC, prove also ADC is acute, and BD > DC. 12. The difference between any two sides of a triangle is less than the third side. 13. AB is a diameter of a circle, centre O; C is on AB produced beyond B; a line through C cuts the...