 If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides.  A Shorter Geometry - Page xviLimited preview - About this book
 | University of Sydney - 1904
...iu-radius and the circum-radius respectively measure 1 ft. and " ft. 1 in. 7. Equal triangles, which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional. 8. Find the weight of a conical... | |
 | Euclid - Euclid's Elements - 1904 - 456 pages
...first. [Book vi. Def. 4.] PROPOSITION 14. THEOREM. Parallelograms which are equal in area, and which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional. Conversely, parallelograms which... | |
 | 1905
...the tangent. ((/) About a given circle circumscribe a triangle equiangular to a given triangle. (e) If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles are similar. '2. ABCD, AEFG are two squares so placed... | |
 | 1906
...; Failed, 21 ; Total, 94. The work in this Stage quite reaches the standard of last year. A. Q. 41. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, show that the triangles are equiangular to one another, and that those... | |
 | 1907
...rectilineal figure which shall be similar to one, and equal to another given rectilineal figure. 4. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals ; the remaining angles are equal, each to each, viz., those which are... | |
 | University of New Zealand - 1907
...parallel to one side of a triangle, the other sides are divided proportionally; and the converse. It' two triangles have one angle of the one equal to one angle of the other, and the sides about their equal angles proportional, the triangles are similar. The internal bisector of an angle of a... | |
 | University of Allahabad - 1908
...converse. If two triangles are equiangular, their corresponding ģidee are proportional ; and the converse. If two triangles have one angle of the one equal to...angle of the other, and the sides about these equal angleĢ proportional, the triangles are similar. The internal bisector of an angle of a triangle divides... | |
 | Great Britain. Education Department. Department of Science and Art - 1908
...angles ABC, DEF are equal, and the angles ACB, DFE are supplementary ; show that AB : DE = AC: DF. If two triangles have one angle of the one equal to one angle of the other, and the sides about one other angle in each proportional, so that the sides opposite equal angles correspond, show that... | |
 | Walter Percy Workman - Geometry - 1908
...thenproveT.il andT.llcby means of Ar.6. 309. THEOREM [Ar.7.]. — It two triangles (or two parallelograms) have one angle of the one equal to one angle of the other, their areas are in the ratio of the products of tbe •ides containing the equal angles. (i) In Fig.... | |
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