 | Euclides - 1884 - 214 pages
...coincide with AE, G. and is parallel to BC. Therefore, equal triangles &c. QED PROPOSITION XL. THEOREM. Equal triangles, on equal bases, in the same straight...the same side of it, are between the same parallels. GIVEN that the triangles ABC and DEF are equal, and on the equal bases BC, EF, which are in the same... | |
 | Association for the improvement of geometrical teaching - Geometry, Modern - 1884 - 150 pages
...are also equal. COR. 3. If two equal triangles stand on the same base and on the same side of it, or on equal bases in the same straight line and on the same side of that straight line, the line joining their vertices is parallel to the base or to that straight line.... | |
 | Mathematical association - 1884 - 146 pages
...are also equal. COR. 3. If two equal triangles stand on the same base and on the same side of it, or on equal bases in the same straight line and on the same side of that straight line, the line joining their vertices is parallel to the base or to that straight line.... | |
 | Education - 1884 - 708 pages
...BA=BE, but BE = AC. Л the triangle ABC is isosceles. Q- b- °2. Equal triangles upon the same base and on the same side of it are between the same parallels. Prop. 39, Bk. I. 3. To a given straight line to apply a parallelogram, which shall be equal to a given... | |
 | Euclides - 1884 - 434 pages
...Prove the proposition for the case when the points D and E coincide. 2. Equal ||m8 on the same base and on the same side of it are between the same parallels. 3. If through the vertices of a triangle straight lines be drawn || the opposite sides, and produced... | |
 | Euclides - 1884 - 182 pages
...two sides of the quadrilateral are parallel to one another. (10) 10. Equal triangles on the same base and on the same side of it are between the same parallels. If a quadrilateral is divided into four equal triangles by its diagonals, show that it is a parallelogram.... | |
 | Euclid, John Casey - Euclid's Elements - 1885 - 340 pages
...equal to half the trapezium. PEOP. XXXIX.— THEOREM. Equal triangles (BAC, BDC) on the same bose (BC) and on the same side of it are between the same parallels. Dem. — Join AD. Then if AD be not parallel to BC, let AE be parallel to it, and let it cut BD in... | |
 | George Bruce Halsted - Geometry - 1885 - 389 pages
...CONCLUSION. AB + AC<A'B + AC. PROOF. AA || BC. (253. INVERSE. Equivalent triangles on the same base, and on the same side of it, are between the same parallels.) Draw CND _L AA \ meeting BA produced in D. Join A'D. 4NAC = 4ACB, (168. If a transversal cuts two parallels,... | |
 | United States. Congress. Senate - United States - 1880 - 1304 pages
...invariable. Under what conditions will this difference be /ею :' 2. Equal triangles on the same base, and on the same side of it, are between the same parallels. The sides .11! and .K'of a triangle are bisected in I) and E respectively, and RE, CD are produced... | |
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Equal triangles, on equal bases, in the same straight line, and on the same side of it, are between the same parallels. Let... 
