...Area of triangle = | x base x perpendicular height = \bh <s— — —— — • —SB^ Triangles on the same base and between the same parallels are equal in area. The line joining the apex of a triangle to the middle point of the opposite side is called a...

...perpendicular and taking the two cases, of which the first is easy and the second hard). (iii) Triangles on the same base and between the same parallels are equal in area (deduced from (ii) since each is given numerically by ?, base x height). (iv) The converse to...

...equal to the area of the parallelogram formed by 72 and the induced current i, since parallelograms on the same base and between the same parallels are equal in area. But if the reactance of the shading coil is negligible compared with its resistance i oc /$2...

...in F, and F is joined to B. Prove that the angles BFA. EFA are equal. 3. Prove that parallelograms on the same base and between the same parallels are equal in area. ABCD, AEFG are two parallelograms having a common point at A, and having the vertex E on BC,...

...Now, parallelogram PRQiPi has base PR and lies between the parallels PR and AB. Since parallelograms on the same base and between the same parallels are equal in area, another parallelogram of area x would be PRJB determined by a line JRK through R parallel to...

...other two sides, then the triangle is a right angled triangle. 2.2 Area Properties: (i) Parallelograms on the same base and between the same parallels are equal in area. (ii) The area of a parallelogram is equal to the area of a rectangle on the same base and of...

...AB.} THE AREA GROUP OF PROPOSITIONS The fundamental proposition of this section is that 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...

...equal, the corresponding intercepts on any other transversal are also equal. Areas * 1. Parallelograms on the same base and between the same parallels are equal in area. 2. Triangles on the same base and between the same parallels are equal in area. 3. Triangles...

...is substituted for the rectangle. Thus we may prove directly the following theorem : Parallelograms on the same base and between the same parallels are equal in area. EXERCISE 7 (a) 1. Find the areas of the following parallelograms: (a) Base 2-5 in., altitude...

...seven questions in Geometry and five in Trigonometry to be attempted.) 1. Prove that parallelograms on the same base and between the same parallels are equal in area, and hence show that a similar proposition is true of triangles. Construct a rectilineal figure...