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" Prove that parallelograms on the same base and between the same parallels are equal in area. "
A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ... - Page 44
by Nathan Scholfield - 1845
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Sessional Papers, Volume 22, Part 2

Great Britain. Parliament. House of Commons - Great Britain - 1900 - 686 pages
...angles shall be equal to one another. .10. Define parallel straight lines and prove that parallelograms on the same base and between the same parallels are equal in area. 11. A square field contains 15 ac. 2 ro. 20 per.; find the length of a path crossing it diagonally....
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A Text-book of Euclid's Elements for the Use of Schools. Books I.-VI ..., Book 1

Euclid, Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 330 pages
...Parallelograms on equal bases and of equal altitudes are equal in area. PROPOSITION 37. THEOREM. Triangles on the same base, and between the same parallels, are equal in area. Let the triangles ABC, DEC be upon the same base BC, and between the same parallels BC, AD. Then...
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Report of the Department of Education for the Year ...

Manitoba. Department of Education - Education - 1900 - 558 pages
...base BC ; prove that ABDC is a parallelogram. 6. Define a parallelogram. Prove that parallelograms on the same base and between the same parallels are equal in area. Construct a rectangle equal to a given parallelogram. 7. The complements of the parallelograms...
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

Eldred John Brooksmith - Mathematics - 1901 - 368 pages
...Examination may be used in the solution of problems and riders. 1. Prove that two triangles standing on the same base and between the same parallels are equal in area. Hence show that if two triangles have two sides of the one equal to two sides of the other and...
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A Text-book of Euclid's Elements for the Use of Schools, Book 1

Euclid - Euclid's Elements - 1904 - 488 pages
...is equal in area to a rectangle of equal base and equal altitude. PROPOSITION 37. THEOREM. Triangles on the same base, and between the same parallels, are equal in area. Let the triangles ABC, DBC be upon the same base BC, and between the same parallels BC, AD. Then...
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A Manual of Carpentry and Joinery

J. W. Riley - Carpentry - 1905 - 518 pages
...area = base xr — c S— . 2i The shape of the triangle does not affect the result, as all triangles on the same base and between the same parallels are equal in area. The area of a triangle can also be determined by the following formula : \^s(s - a)(s - b)(x...
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Annual Report - Dept. of Education

Saskatchewan. Department of Education - Education - 1906 - 188 pages
...sides of a triangle is parallel to the third side and equals the half of it. (d) As parallelograms on the same base and between the same parallels are equal in area (1.35) show how this proposition affords a means of measuring the area of a parallelogram, triangle,...
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A School Course of Mathematics

David Mair - Mathematics - 1907 - 412 pages
...position of this point, and give a geometrical proof of the above statement. 19. Prove that parallelograms on the same base and between the same parallels are equal in area. How could this be verified by means of a pack of cards or a pile of slates 1 From this illustration...
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The Dublin University Calendar, Volume 1

Trinity College (Dublin, Ireland) - 1908 - 574 pages
...parallel to one of its sides, construct a similar figure. Theoretical. 4. Trove that parallelograms on the same base and between the same parallels are equal in area. 5. In any triangle, prove that the square on the side opposite an acute angle is less than the...
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A School Geometry, Parts 1-4

Henry Sinclair Hall - 1908 - 286 pages
...Areas. DEFINITIONS 99 THEOREM 23. AREA OF A RECTANGLE. 100 THEOREM 24. [Euc. I. 3o.] Parallelograms on the same base and between the same parallels are equal in area. 104 AREA OF A PARALLELOGRAM - - - . - - - - 105 THEOREM 25. AREA OF A TRIANGLE. 106 THEOREM 26....
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