| Education - 1903
...converse. If two triangles are equiangular their corresponding sides are proportional ; and the converse. **If two triangles have one angle of the one equal to one angle of the other and the sides about** these equal angles proportional, the triangles are similar. The internal bisector of an angle of a... | |
| Charles Godfrey, Arthur Warry Siddons - Geometry - 1903 - 355 pages
...§AB, OQ = J5 AC ; join PQ ; measure L.' P, Q, and compare them with L.' B, C. =o fig. 313. THEOREM 5. **If two triangles have one angle of the one equal to one angle of the other and the sides about** these equal angles proportional, the triangles are similar. fig. 314. Data ABC, DEF are two triangles... | |
| 1903
...that the square on DE is equal to twice the rectangle contained by the radii of the two circles. 4. **If two triangles have one angle of the one equal to one** an^le of the other, and the sides about the equal angles proportionals, show that the triangles are... | |
| 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... | |
| 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... | |
| 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...the sides about the equal angles proportionals, the** triangles are similar. '2. ABCD, AEFG are two squares so placed that the angles at A coincide. Show... | |
| 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...and the sides about the equal angles proportionals,** show that the triangles are equiangular to one another, and that those angles are equal which are opposite... | |
| 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...those which are opposite to the homologous sides.** 5. Parallelograms upon the same base and between the same parallels are equal to one another. SECTION... | |
| |