Notes On The Topology Of Complex Singularities by Nicolaescu

By Nicolaescu

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Every equilateral triangle also isosceles? la Is every isosceles triangle also equilateral ? Is an obtuse triangle ever your answers. Is a right triangle ever isosceles? 2. Draw isosceles? figures to illustrate In the figure on page i determine by measuring sides which of 3. HNP, LKW, IHN, MIJ, KVU, OKJ, LVW, the triangles which are celes, Determine whether 4. and which are equilateral, vertices of a triangle K, V of the same figure whether /, 0, G may be. /, also ; are isos- scalene. may be the Pick out ten obtuse triangles in this figure; also ten acute 5.

117. 45 // in two triangles two sides of the to two sides of the other, but one are equal respectively the included angle of the first is greater than the included angle of the second, then the third side of the is first greater than the third side of the second. A ABC Given and To prove that Proof: A'BC which in AB=A'&, BC = BC and AC > A'c'. Place Aa'b'c' on A ABC so that a'b' coincides with its equal AB and C' is on the same side of AB as C. Draw DC'. Let BD bisect Z g'bc, meeting AC in I) .

Therefore CO (or CD} It in O. the required perpendicular bisector of AB. this, Hence and \, CD meeting ^B Hence By what C -i'B equally is B. the segment To prove points, l argument (o) are AAOC^ABOC. Study this outline with care. What is wanted is the last result (rf). Notice that (d) is obtained from (c), (c) from (6), and (6) from (o). Thus each step depends on the one preceding, and would be imposTo understand clearly the order of the steps in a sible without it. proof as shown by such an outline ing of great importance in master- is it.

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