Robbin's New Plane Geometry

Cover Robbin's New Plane Geometry
Robbin's New Plane Geometry
Edward Rutledge Robbins
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The area of a rhombus equals half the product of its diagonals.
Ex. 6. The diagonals of a parallelogram divide it into four triangles of equal areas.
Ex. 7. The diagonals of a trapezoid divide it into four triangles, two of which are similar and the other two have equal areas.
Ex. 8. If a parallelogram has half the base and half the altitude of a triangle, its area is half the area of the triangle.
Ex. 9. The line joining the midpoints of two sides of a triangle forms a triangle whose area is o
...ne fourth the area of the original triangle.
Digitized by VjOOQ IC AEEAS 199 Ex. 10. The line joining the midpoints of two adjacent sides of a parallelogram cuts off a triangle whose area is one eighth of the area of the parallelogram.
Ex. 11. If one diagonal of a quadrilateral bi- sects the other, it also divides the quadrilateral into two triangles having equal areas.
To Prove : A abc = A ADC. o Ex. 12. Either diagonal of a trapezoid divides the figure into two tri- angles the ratio of which is equal to the ratio of the bases of the trapezoid.


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