...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...

...; 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...

...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...

...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...

...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...

...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,...

...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...

...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....

...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...

...respectively, find the length of the radius of the inscribed circle. 16. Prove that parallelograms, and also triangles, on the same base and between the same parallels, are equal in area. L and M are two given parallel straight lines, and P and Q two given points. Show how to draw...