...upon the same base and between the same parallels are equal to one another. Prop. 37. — Theorem. Triangles upon the same base and between the same parallels are equal to one another. Prop. 47. — Theorem. In any right angled trinngle, the square which is described upon the side subtending...

...Given the vertical angle, and a side to construct the triangle. 3. Prop. 35. Theorem. Parallelograms upon the same base and between the same parallels are equal to one another. Shew this is equally true of triangles. 4. Prop. 44. — Problem. To a given straight line to apply...

...respects oblique parallelograms abo. By Euclid, Book I, Prop. 35, it is established that «parallelograms upon the same base and between the same parallels are equal to one another." Now, the perpendicular distance, D С, between the sides, DF and В С, of the oblique parallelogram...

...BC divides the parallelogram ACI>B into two equal parts. QED PROP. XXXV.— THEOREM. Parallelograms upon the same base, and between the same parallels, are equal to each other. (References— Prop. I 4, 29, 34 ; ax. 1, 3, 6.) Let the parallelograms ABCD, EBCF, be...

...two equal parts. Wherefore, the opposite sides &c. QED PROPOSITION 35. THEOREM. Parallelograms on the same base, and between the same parallels, are equal to one another. Let the parallelograms ABCD, EBCF be on the same base BC, and between the sameparallels AF, BC : the...

...two equal parts. Wherefore, the opposite aides &c. QED PROPOSITION 35. THEOREM. Parallelograms on the same base, and between the same parallels, are equal to one another. Let the parallelograms A BCD, EBCF be on the same base BC, and between the sameparallels AF,BC: the...

...triangle be produced, the exterior nngle is greater than cither of the interior opposite angles 15 i 2. Triangles upon the same base, and between the same parallels, are equal to one another 15 3. In any right -angled triangle, the square \rhieh is described upon the side subtending the right...

...the parallelogram A CBF. Then ACBF = DBCE. But ABC is half of ACBF; therefore of DBCE. THEOREM IV. Triangles upon the same base and between the same parallels are equal. For each is half of any parallelogram on that base and between those parallels. COR. 1. Triangles upon...

...not necessarily be of the same shape to be of equal area, and by Euclid* (Book I., prop, xxxvii.), " Triangles upon the same base, and between the same parallels, are equal." If, therefore, lines be drawn from ABCDE and F to G, five triangles will be formed, having the same...

...Extract the square root of 141 • 7 to two places of decimals. (10.) *3. Show that parallelograms and triangles upon the same base and between the same parallels are equal to one another. (10.) 23 5. Angles in the same segment of a circle are equal to one another. *6. Divide a" — SaV...