| Mathematical association - 1883
...two adjoining sides of the one respectively equal to two adjoining sides of the other, and likewise **an angle of the one equal to an angle of the other;** the parallelograms are identically equal. [By Superposition.] COR. Two rectangles are equal, if two... | |
| Euclides - 1885
...by paira of adjacent sides. Triangles which have one angle of the one equal or supplementary to one **angle of the other are to one another as the rectangles contained by the sides about those angles.** 5. From the similar AS ABK, EBH, AK:EH = AB:EB. f A JT - f^ff } But rAC: r EF = j ££ ; ™ I , by... | |
| Mathematical association - 1884
...two adjoining: sides of the one respectively equal to two adjoining sides of the other, and likewise **an ang:le of the one equal to an angle of the other** ; the parallelograms are identically equal. Let ABCD, EFGH be two parallelograms having the angle ABC... | |
| Evan Wilhelm Evans - Geometry - 1884 - 149 pages
...; hence, it is also similar to DFE. Therefore, two triangles, etc. THEOREM XI. Two triangles having **an angle of the one equal to an angle of the other,** and the sides about those angles proportional, are similar. Let the two triangles ABC, DEF, have the... | |
| William Kingdon Clifford - Mathematics - 1885 - 310 pages
...proposition about parallel lines.1 The first of these deductions will now show us that if two triangles **have an angle of the one equal to an angle of the other** and the sides containing these angles respectively equal, they must be equal in all particulars. For... | |
| Lewis Carroll - Geometry - 1885 - 318 pages
...have two adjacent sides of the one respectively equal to two adjacent sides of the other, and likewise **an angle of the one equal to an angle of the other** ; the Parallelograms are identically equal.' This might be a useful exercise to set ; but really it... | |
| William Chauvenet - Geometry - 1887 - 331 pages
...B'C' A'B" hence AD BC A'D' X B'C' and we have ABC A' B' C' EXERCISE. Theorem. — Two triangles having **an angle of the one equal to an angle of the other are to** each other as the products of the sides including the equal angles. Suggestion. Let ADE and ABC be... | |
| Benjamin Franklin Finkel - Mathematics - 1888 - 518 pages
...5. Two polygons that are similar to a third polygon ale similar to each other. 6. If two triangles **have an angle of the one equal to an angle of the other,** their areas are to each other as the rectangles of the sides including those angles. 7. The ratio of... | |
| Dalhousie University - 1888
...sides, the solids contained by the alternate segments of these lines are equal. 3. If two triangles **have an angle of the one equal to an angle of the other,** and have their areas proportional to the squares of the side* opposite these equal angles, they must... | |
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