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" Prove that parallelograms on the same base and between the same parallels are equal in area. "
Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ... - Page 36
by Nathan Scholfield - 1845
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Proceedings - Insurance Institute of Toronto

Insurance Institute of Toronto - 1904 - 248 pages
...exterior angle shall be greater than either of the interior opposite angles. (1-16.) 2. Parallelograms on the same base and between the same parallels are equal in area. (1-35.) 3. Describe a parallelogram that shall be equal to a given triangle and have one of its...
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a gemoetry for schools

356 pages
...results are at once deduced : (i) The area of a parallelogram = height x base. (ii) Parallelograms on the same base and between the same parallels are equal in area. II. The area of a triangle = Iialf that of a rectangle on the same base and of the same height....
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The Hellenistic Philosophers: Volume 1, Translations of the Principal ...

A. A. Long, D. N. Sedley - Philosophy - 1987 - 352 pages
...Euclid's Elements I 395,13-18 (SVF 2.365, part) Such theorems [ie as the theorem that parallelograms on the same base and between the same parallels are equal in area], Geminus reports, were compared by Chrysippus to the Ideas [cf. 30]. For just as the Ideas encompass...
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Challenge and Thrill of Pre-College Mathematics

V Krishnamurthy, C R Pranesachar - Mathematics - 2007 - 708 pages
...from A to B/ and C/. Prove that XY is parallel to BC. 3.5 SIMILAR TRIANGLES Theorem 27 Parallelograms on the same base and between the same parallels are equal in area. Proof Let ABCD and ABXY be two parallelograms having the same base AB and lying between the same...
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Mathematics for The Services

100 pages
...equal in area to the parallelogram and having for one of its diagonals the line AC. [Hint. Triangles on the same base and between the same parallels are equal in area.] 7. (a) If the base of a triangle is 2 in. and its altitude is 1 J in., state clearly what is...
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Definitions and Formulae in Mathematics IX & X

Ravi Kumar - Mathematics - 2006 - 152 pages
...and between the same parallels, AQ and DR, then ar (||gm ABCD) = ar (||gm PQRS). Theorem 3. Triangles on the same base and between the same parallels are equal in area, ie, in two AABC and DBC on the same base BC and between the same parallel lines BC and AD, then...
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The New Geometry: Form One

G. P. West - Geometry - 1965 - 362 pages
...are the base and height ; from this we deduce a theorem analogous to the theorem that parallelograms on the same base and between the same parallels are equal in area. Parallelepipeds on equal bases and of the same height are equal in volume. Similarly if we had...
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A Shorter Geometry

464 pages
...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 triangles...
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