 | Mathematical Association - 1923 - 88 pàgines
...METHOD. (i) Parallelograms on the same base and between the same parallels are equal in area. (ii) Triangles on the same base and between the same parallels are equal in area (proved by duplicating the triangles and using (i) ). (iii) The converse to (ii) (proved by... | |
 | Ivor Grattan-Guinness, Gerard Bornet - 1997 - 310 pàgines
...geometry exhibited in the form of propositions are universal ie they have universal subjects. Ex. All triangles on the same base and between the same parallels are equal. All right angled triangles have this property that the square of the hypothenuse is equal to the squares... | |
 | Education Department - 1879 - 1118 pàgines
...bisects it. If the diagonal also bisects the angles, show that the parallelogram is a rhombus. 2. Show that triangles on the same, base and between the same parallels are equal to each other. Hence show that a trapezium is equal in area to a triangle whose vertical height is... | |
 | 464 pàgines
...opposite sides of a straight line AB; join DQ, CP: prove that CDQP is a parallelogram. 4. (a) Prove that triangles on the same base and between the same parallels are equal in area. (6) FGH is a triangle, K is the mid.point of GH, and P is any point on FK ; prove that the... | |
 | 1897 - 734 pàgines
...; the method is mathematically accurate, and is based upon a familiar proposition of Euclid, viz., that triangles on the same base, and between the same parallels, are equal (vide Euc. I. 37). Suppose it is required to reduce the figure ABCDEF — which is supposed to be plotted... | |
 | Thomas Hadyn Ward Hill - 190 pàgines
...parallelograms on the same base and between the same parallels are equal in area. From this we have that triangles on the same base and between the same parallels are equal in area, and the converse; and also expressions for the areas of parallelograms, triangles, quadrilaterals... | |
 | 1904 - 500 pàgines
...opinion of the speaker, should be given to boys as soon as they reach Euc. I. 35, 37 [parallelograms (triangles) on the same base, and between the same parallels, are equal to one another], and they then get for commensurable bases Euc. VI. 1 [triangles and parallelograms... | |
 | 1965 - 232 pàgines
...depends only on its base and altitude. [Exercises 7 (a) and 7 (6) may now be taken.] Theorem 5 a. (i) Triangles on the same base and between the same parallels are equal in area. (ii) Conversely, if two triangles with equal areas stand on the same side of a common base,... | |
 | 666 pàgines
...ABCF)= Ar. (A BCE) + Ar.( quad. ABCF) => Area of square ABCD = Area of parallelogram ABEF Theorem 19.2 Triangles on the same base and between the same parallels are equal in area. Given : Triangles ABC and ABD on the same base AB and between the same parallels, AB parallel... | |
 | 100 pàgines
...rectangle equal in area to the parallelogram and having for one of its diagonals the line AC. [Hint. Triangles on the same base and between the same parallels are equal in area.] 7. (a) If the base of a triangle is 2 in. and its altitude is 1 J in., state clearly what... | |
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... that triangles on the same base and between the same parallels are equal... 
