| Euclides - 1874 - 120 pages
...The diagonals of a parallelogram bisect each other. PROPOSITION 35. THEOREM. Parallelograms on the **same base, and between the same parallels, are equal to one another. .. Let the** parallelograms ABCD, EBCFbe on the '• same base BC, and between the same parallels AF, BC: the parallelogram... | |
| Braithwaite Arnett - 1874 - 130 pages
...to a given straight line of unlimited length from a given point without it. 2. Parallelograms on the **same base and between the same parallels are equal to one another.** 3. If a straight line be bisected, and produced to any point, the rectangle contained by the whole... | |
| Edward Atkins - 1876 - 130 pages
...two equal parts. Therefore, the opposite sides, &c. QED Proposition 35. — Theorem. Parallelograms **upon the same base, and between the same 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... | |
| Robert Potts - Geometry, Plane - 1876 - 446 pages
...of the 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... | |
| William George Spencer - Geometry - 1876 - 118 pages
...make two 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... | |
| Henry Major - 1876 - 784 pages
...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... | |
| Education Department,London - 1876 - 1010 pages
...? Construct the triangle when each side is equal to half the sum of the other two. SECTION III. 2. **Triangles upon the same base and between the same parallels are equal.** A line drawn through the middle points of the sides of a triangle is parallel to the base. 3. In any... | |
| James Martin (of the Wedgwood inst, Burslem.) - 1876 - 334 pages
...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... | |
| 1876 - 400 pages
...equal to two right angles. What ratio does the angle of a regular hexagon bear to a rig] it angle? 2. **Triangles upon the same base and between the same parallels are equal.** A line drawn through the middle points of the sides of the triangle is parallel to the base. 3. In... | |
| 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... | |
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