| Marianne Nops - 1882 - 278 pages
...easier. Only one case is given by Euclid. SUMMARY OF PROPOSITION XXXV., THEOREM 25. Parallelograms on the same base and between the same parallels are equal in area. Cons. — Nil. Case I. Each \^m is double of A DEC (I. 34). .-. Hg™™ are equal. Cases II.... | |
| 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... | |
| 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.... | |
| 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... | |
| 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.... | |
| 1894 - 1136 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... | |
| 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... | |
| 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... | |
| Great Britain. Board of Education - Education - 1900 - 906 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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