Elements of Geometry

Cover Elements of Geometry
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8. The number of sides of a polygon may be found when the sum of its interior angles is three times the sum of its exterior angles.
9. Show how to determine a line parallel to the parallels of a trapezoid that will bisect its area.
10. The lines joining the middle points of the adjacent sides of any quadrangle will form a parallelogram.
11. The lines joining the middle points of the adjacent sides of a rectangle will be a rhombus.
FIG. 176.
12. The lines joining the middle points of the adjacen
...t sides of a rhombus will be a rectangle.
13. If two A, A and B, of the A ABO be bisected, and a line DE be drawn through /, || to AS, DE = AD+ BE.
FIG. 17T.
14. The sum of the perpendicu- lars from any point in the base of an isosceles triangle to the equal sides is constant, and equals the altitude from one of the equal angles.
Analysis. If DE + DF= AH, and if we should through D draw a parallel to CB, it would determine KH = DF, and in order that the proposition be true, AK would have to equal DE.


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