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" Prove that parallelograms on the same base and between the same parallels are equal in area. "
Examination Papers for Science Schools and Classes - Page 23
by Great Britain. Education Department. Department of Science and Art - 1882
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

Eldred John Brooksmith - 1904 - 378 pages
...driven forward 4 ft. a day. How many cubic yards of earth are excavated in a day ? 2. Show that two parallelograms on the same base and between the same parallels are equal in area. As an illustration, draw on the squared paper a rectangle with base 2 ins. long and height...
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Mathematical and Physical Papers, Volume 5

George Gabriel Stokes - Hydrodynamics - 1905 - 403 pages
...lie between 0 and 1, prove that ^ — — >ac. I — a 3. In the figure of Euclid, Book i. Prop. 35 (Parallelograms on the same base and between the same parallels are equal), if two diagonals be drawn to the two parallelograms respectively, one from each extremity of the base,...
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Mathematical and Physical Papers, Volume 5

George Gabriel Stokes - Mathematics - 1905 - 412 pages
...x both lie between 0 and 1, prove that _ >x. 1 — o/ 3. In the figure of Euclid, Book I. Prop. 35 (Parallelograms on the same base and between the same parallels are equal), if two diagonals be drawn to the two parallelograms respectively, one from each extremity of the base,...
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A Manual of Carpentry and Joinery

J. W. Riley - Carpentry - 1905 - 522 pages
...= ^—f- = 13-93 = 139'3 cm. ; the area of the triangle in sq. dcm. = ^ = 111'44. Jf Triangles and parallelograms on the same base and between the same parallels are equal in area. Tims, in Fig. 157 the triangles ABC, DBC, and EBC, all being upon the same base BC and between...
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Annual Report - Dept. of Education

Saskatchewan. Department of Education - Education - 1906 - 188 pages
...points of any two 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,...
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A School Course of Mathematics

David Mair - Mathematics - 1907 - 412 pages
...you like the 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) - 1907 - 536 pages
...expected to make at least ONE of the abafe constructions. THEORETICAL GEOMETRY. 3. Prove that any two parallelograms on the same base and between the same parallels are equal. 4. State the axiom which you use in establishing the properties of parallel lines, and prove any proposition...
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The Dublin University Calendar, Volume 1

Trinity College (Dublin, Ireland) - 1908 - 574 pages
...it, shorter than and 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...
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Intermediate Geometry: Being Sections V and VI of "geometry, Theoretical and ...

Walter Percy Workman - Geometry - 1908 - 228 pages
...The area of a rectangle is given by the product of the lengths of two adjacent sides 178 Ar.2. — Parallelograms on the same base and between the same parallels are equal in area (Euc. I. So) 184 Ar.3. — If a parallelogram and a triangle be on the same base and between...
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Plane and Solid Geometry

Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...proportional between the whole secant and its external segment. THEOREMS ON AREAS OF POLYGONS 383. Parallelograms on the same base and between the same parallels are equal. 385. The areas of two rectangles having equal altitudes are in the same ratio as their bases. 389....
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