 | Edward Atkins - 1876 - 130 pages
...parallelogram EFGH (Ax. 1). Therefore, parallelograms, &c. QED Proposition 37. — Theorem. Triangles upon the same base, and between the same parallels, are equal to one another. Let the triangles ABC, DBC be on the same base BC, and between the same parallels AD, BC ; The triangle ABC... | |
 | Henry Major - 1876 - 784 pages
...side together equal to two right angles, the two straight lines shall be parallel to one another. 8. Parallelograms upon the same base, and between the same parallels, are equal to one another. Are the parallelograms equal in all respects ? 1. Simplify 1£ — | -j 1 — *-(*— §) >• , and... | |
 | William George Spencer - Geometry - 1876 - 118 pages
...triangles that shall be equal to each other, and yet not similar ? 137. Can you show that all triangles upon the same base and between the same parallels are equal to one another 'i 138. Can you place a circle, whose radius is 1J inch, so that its circumference may touch two points... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...one shall be equal to the angle contained by the two sides, equal to them, of the other. 2. Triangles upon the same base, and between the same parallels, are equal to one another. 3. If the square described upon one of the sides of a triangle be equal to the squares described upon... | |
 | James Martin (of the Wedgwood inst, Burslem.) - 1876 - 334 pages
...student enters on the following problems he should thoroughly master the subjoined theorems.) (A.) "Parallelograms upon the same base, and between the same parallels, are equal to each other" (in area). — Euc. I., 35. Ex. ABCD, DBCF— NOTE 1. — " Between the same parallels... | |
 | University of Madras - 1876 - 580 pages
...D. Prove that the exterior angle ACD is greater than the angle ABC. III. Prove that triangles on the same base and between the same parallels are equal to one another. (a) Two equal triangles have two sides of the one equal to two sides of the other. What con elusion... | |
 | Medicine - 1876 - 610 pages
...contained angles are equal, and if the third sides are unequal, the contained angles are unequal. 3. Parallelograms upon the same base and between the same parallels are equal. 2. If a straight line falling upon two other straight lines makes the alternate angles equal, those... | |
 | Edward Atkins - 1877 - 72 pages
...parallelogram ABCD into two equal parts. Therefore, the opposite sides, &c. QED Proposition 35. — Theorem. Parallelograms upon the same base, and between...parallels, are equal to one another. Let the parallelograms ABCD, EBCF be on the same base BC, and between the same parallels AF, BC ; The parallelogram ABCD shall... | |
 | D. Tierney - 1877 - 126 pages
...described would not intersect, and therefore the construction for the triangle required would fail. 2. Parallelograms upon the same base, and between the same parallels, are equal to one another. Shew that if two triangles have two sides of the one equal to two sides of the other, each to each,... | |
 | William George Spencer - Geometry - 1876 - 118 pages
...triangles that shall be equal to each other, and yet not similar ? 137. Can you show that all triangles upon the same base and between the same parallels are equal to one another ? 138. Can you place a circle, whose radius is \\ inch, so that its circumference may touch two points... | |
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PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another... 
