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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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The papers set at the professional preliminary examination

College of preceptors - 1882 - 528 pages
...two sides of a triangle and the third side. 3. Define a parallelogram ; and show that parallelograms on the same base and between the same parallels are equal in area. Enunciate a converse of this proposition. 4. Define an acute-angled triangle, an obtuse-angled...
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Cambridge University Examination Papers

University of Cambridge - 1884 - 624 pages
...angles shall be equal, each to «*acb. namely tboee to which the equal sides are opposite. 9. Triangles on the same base, and between the same parallels, are equal. In the sides В С, CD of a parallelogram AB С D points P, Q are taken such that PQ i» parallel to BD....
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884 - 434 pages
...Equal |]m8 situated between the same parallels have equal bases. PROPOSITTON 37. THEOREM. Triangles on the same base and between the same parallels are equal in area. BC Let ABC, DBC be triangles on the same base BC, and between the same parallels AD, BC: it is...
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Examinations Papers

1885 - 522 pages
...meet in B. Prove that the angles ABC, ABD are together equal to two right angles. 2. Parallelograms on the same base and between the same parallels are equal in area. 3. Describe a rectangle which shall be equal to a given parallelogram. 4. C is a point in the...
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Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - Geometry - 1890 - 442 pages
...and for similar reasons, a CDRS = a ABRS. .-. a ABPQ = a CDRS. Proposition 37. THEOREM — Triangles on the same base, and between the same parallels, are equal in area. Draw AX j| to BP, and BY || to AQ ; and let them meet PQ, produced both ways, in X and Y respectively....
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Annual Report

1894 - 1174 pages
...converse of the following: 1. The angles at the base of an isosceles triangle are equal. '2. Triangles on the same base and between the same parallels are equal in area. 10. In the triangle PQRQ^R prove PR+QR greater than PQ. 11. If a straight line cutting two other...
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Calendar ...

University College, Galway - 1896 - 430 pages
...+ 1. 5' Simplify (*+l)H (*-!)». 6. Solve the equation x + 5 x - 6 x + 3 ~ x - 9' 7. Parallelograms on the same base and between the same parallels are equal in area. 8. If a straight line is bisected and also divided unequally the sum of the squares on the unequal...
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Report of the Council of Public Instruction of the North-West Territories of ...

Northwest Territories Council of Public Instruction - 1897 - 628 pages
...parallel ; (ii) with one pair parallel ; (iii) with two pairs parallel. (J) Prove that parallelograms on the same base and between the same parallels are equal in area. I. 35. (f) Point out the uses of proposition (I) in mensuration. (d) Prove that if a square and...
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Science Examination Papers

Great Britain. Education Department. Department of Science and Art - Examinations - 1899 - 348 pages
...figure equals seven-eighths of two right angles, find the number of sides. (12.) 10. Show that triangles on the same base and between the same parallels are equal in area. ABCD is a parallelogram, and P is a point within the angle formed by DC and the prolongation...
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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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