Elementary plane geometry : inductive and deductive / by Alfred Baker . he three angles in each ofthese triangles is two right angles, or 180°. 4. It is proposed to show that the sum of the threeangles of any triangle must be two right angles, or180°: Construct a triangleABC, and place a pencilin the position the pencil throughthe angle BCA, in thedirection indicated bythe arrow head, to theposition EC. Slide italong CA, towards A, tothe position FG, and turn it through the angle CAB,to the position HK. Slide it along AB to the positionBL, and tui^n it thiough the angle B, to the posit
Elementary plane geometry : inductive and deductive / by Alfred Baker . he three angles in each ofthese triangles is two right angles, or 180°. 4. It is proposed to show that the sum of the threeangles of any triangle must be two right angles, or180°: Construct a triangleABC, and place a pencilin the position the pencil throughthe angle BCA, in thedirection indicated bythe arrow head, to theposition EC. Slide italong CA, towards A, tothe position FG, and turn it through the angle CAB,to the position HK. Slide it along AB to the positionBL, and tui^n it thiough the angle B, to the positionBM. The pencil has rotated through all the angles of thetriangle. But in its final position BM it points in adirection just opposite to its first position DC, andtherefore must have rotated through 180°. Hence allthe angles of this (which is any) triangle musttogether equal 180, or two right angles. It follows that if two triangles have twoangles in the one equal to two angles in theother, the third angle in one triangle is equalto the third angle in the 26 Geometry. 5. Construct two tiiangles, ABC, DEF, each with baseIJ inch, and angles at the base 79 and 57.
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