 | Moffatt and Paige - 1879 - 506 pages
...squares on the sides. (Note.— Apply Euc. II. 12, 13.) *(S3) The two triangles, formed by drawing lines from any point within a parallelogram to the...extremities of two opposite sides, are together half the parallelogram. * (54) The sum of the squares on the sides of any quadrilateral figure is equal... | |
 | Pupil teachers - 1880 - 1486 pages
...same parallels, the parallelogram shall be double of the triangle. Same proposition. Hence deduce that two triangles formed by drawing straight lines from...point within a parallelogram to the extremities of its opposite sides, are together hall of the parallelogram. Propositions XLH-XLVHI. (inclusive). 42.To... | |
 | 1880 - 594 pages
...was again received with shouts." Euclid. — i. Euc. I. 27. 2. The two triangles, formed by drawing lines from any point within a parallelogram to the...extremities of two opposite sides, are together half the parallelogram. 3. Euc. I. 44. Algebra. — I . Multiply a — b + c — d\sy a -\-bcd, and subtract... | |
 | Moffatt and Paige - 1881 - 176 pages
...to each other ; these two straight lines shall be parallel. 2. The two triangles, formed by drawing lines from any point within a parallelogram to the...extremities of two opposite sides, are together half the parallelogram. 3. To a given straight line to apply a parallelogram, which shall be equal to a... | |
 | John Robertson (LL.D., of Upton Park sch.) - Examinations - 1882 - 152 pages
...parallelogram shall be double of the triangle. 3. To describe a circle about a given square. 4. Prove that the two triangles formed by drawing straight lines...opposite sides, are together half of the parallelogram. 5. If two angles of a triangle be equal to one another, the sides also which subtend or are opposite... | |
 | Franklin Ibach - Geometry - 1882 - 208 pages
...non-parallel sides of a trapezoid to the middle point of the other, is equivalent to half the trapezoid. 8. The two triangles formed by drawing straight lines...point within a parallelogram to the extremities of either pair of opposite sides, are equivalent to half the parallelogram. 9. The bisector of the vertical... | |
 | Seth Thayer Stewart - Geometry - 1891 - 428 pages
...sum of the parallel sides, and whose altitude is the perpendicular distance between those sides. 87. The two triangles formed by drawing straight lines...opposite sides are together half of the parallelogram. 88. If a straight line be drawn from one of the acute angles of a right-angled triangle, bisecting... | |
 | Seth Thayer Stewart - Geometry, Modern - 1891 - 422 pages
...between those sides. 87. Two of the triangles formed by drawing straight lines from any point without a parallelogram to the extremities of two opposite sides are together half of the parallelogram. 88. If a straight line be drawn from one of the acute angles of a right-angled triangle, bisecting... | |
 | Seth Thayer Stewart - Geometry - 1893 - 262 pages
...Д EFC (PI, and В. п., P. III.) ; .-., ABCD = BCFE (Ax. in.); ie, the trapezoid oi of the C3. 87. The two triangles formed by drawing straight lines...opposite sides are together half of the parallelogram. See g 2I3, Ex. 4. 88. If a straight line be drawn from one of the acute angles of a right-angled triangle,... | |
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If from a point, without a parallelogram, there be drawn two straight lines to the extremities of the two opposite sides, between which, when produced, the point does not lie, the difference of the triangles thus formed is equal to half the parallelogram.... 
