 | Mathematical Association - 1923 - 88 σελίδες
...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 σελίδες
...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... | |
 | 464 σελίδες
...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... | |
 | Education Department - 1879 - 1118 σελίδες
...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... | |
 | 1897 - 734 σελίδες
...; 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 σελίδες
...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... | |
 | Ravi Kumar - 2006 - 152 σελίδες
...and PQ and between the same parallels, AQ and DR, then ar (||gm ABCD) = ar (||gm PQRS). Theorem 3. Triangles on the same base and between the same parallels are equal in area, ie, in two AABC and DBC on the same base BC and between the same parallel lines BC and AD,... | |
 | 1904 - 500 σελίδες
...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... | |
 | 356 σελίδες
...BDA F-rect. DAXC) = \ rect. BCXY. It follows that (i) The area of a triangle = £ base x height. (ii) Triangles on the same base and between the same parallels are equal in area. (iii) Equal triangles on the same base and the same side of it are between the same parallels.... | |
 | 100 σελίδες
...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... 
