...of the bisectors to the vertex of the third ^ of the A bisects that third Z. INEQUALITIES THEOREM 16 Any two sides of a triangle are together greater than the third side. B DC Hypothesis. — ABC is a A. To prove that AB + AC> BC. Construction. — Bisect ZA and let the...

..."Indirect Method of Proof" and illustrate it fully by reference to a proposition in Book I. 8 2. (a) Any two sides of a triangle are together greater than the third side. 20 — I. 6 (b) The sum of the distances of any point from the three angular points of a triangle is...

...is, as 12 is to 8. As BC equals 10, EF equals T % of 10 = 6|, and as CA = 8, FD = ^ of 8 = 5 J. X. Any two sides of a triangle are together greater than the third side. XL Parallelograms upon the same base or upon equal bases, 8 C Fio. 41. and between the same parallel,...

...one side be produced the exterior angle equals the sum of the two interior opposite angles. Prop. 7. Any two sides of a triangle are together greater than the third. Prop. 8. Two triangles are congruent (ie are equal in every respect) if they have — (a) two sidea...

...science may not be a postulate in another. In Euclid's development of geometry, the statement that any two sides of a triangle are together greater than the third side is not a postulate, because it is deduced from other statements (postulates) which are avowedly assumed...

...quadrilateral bisect each other, prove that the quadrilateral is a parallelogram. (15) 2. Prove that any two sides of a triangle are together greater than the third side. Show that the diagonals of a quadrilateral are together less than the perimeter of the quadrilateral,...

...are the perpendiculars from A upon these bisectors. Prove that CE is parallel to BD. 3. Prove that any two sides of a triangle are together greater than the third. 4. Two fixed points P and Q are taken, and AB is an unlimited straight line in the same plane as P...

...were hunting Uie wild beasts on horseback. GEOMETRY.— X. • 9 to 11 am, Friday, 25 June, 1915. 1. Any two sides of a triangle are together greater than the third side. 2. Two right-angled triangles which have their hypotenuses equal, and one side of the one equal to...

...of a triangle are unequal, the greater side has the greater angle opposite to it : and the converse. Any two sides of a triangle are together greater than the third. Of all the straight lines that can be drawn to a given straight line from a given point outside it,...

...shortest distance from one point to another is as "the crow flies"; and stated his proposition that any two sides of a triangle are together greater than the third. Ask the average boy to prove this as a general theorem : he will draw a perfect figure, measure the...