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
| Civil service
...proportion. PROP. I. — Triangles of the same altitude are one to the other, as their bases. PROP. VI. — **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... | |
| Robert Potts - Geometry, Plane - 1860 - 361 pages
...triangle ABC is equiangular to the triangle DEF. Wherefore, if the sides, &c. QED PROPOSITION VI. THEOREM. **If two triangles have one angle of the one equal to one angle of the other,** find the sides about the equal angles proportionals, the triangles shaU be equiangular, and shall have... | |
| War office - 1861
...is less than a right angle. 4. To describe an equilateral and equiangular hexagon in a given circle. **5. If two triangles have one angle of the one equal to one angle of the other and the sides about** two other angles proportionals, and if each of the remaining angles be not less than a right angle,... | |
| War office - 1861 - 12 pages
...perpendicular to the line touching the circle. Voluntary Portion. 1. To inscribe a square in a given circle. 2. **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 to one another, and shall have those... | |
| Euclides - 1861
...into one Theorem, Prop. 1, VI, and might also be united here. PROP. 15. — THEOn. Equal angles which **have one angle of the one equal to one angle of the other,** have their sides about the equal angles reciprocally proD. 1 H. &C. 2 7. V. 3 1,V. 4 11, V. 5 Cone.... | |
| Woolwich roy. military acad - 1861
...described on P 0 as diameter will pass through all the points of contact. 8. Equal parallelograms which **have one angle of the one equal to one angle of the other,** have their sides about the equal angles reciprocally proportional, and parallelograms that have one... | |
| University of Cambridge - 1884
...exterior angle made by producing one of the sides through the vertex. 9. Equal parallelograms, which **have one angle of the one equal to one angle of the other,** have their sides about the equal angles reciprocally proportional. WEDNESDAY, December 5, 1883. 12$... | |
| Woolwich roy. military acad - 1884
...in E, shew that AB touches the circumscribing circle of the triangle CDE. 10. 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 ; and triangles which have one angle... | |
| 1884
...a given circle. Inscribe a regular figure of ten sides in a given circle. 3. 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. If one of the said sides in the... | |
| Euclides - 1884
...= ir BC: ir FE; • ||m AB : ||m FE = ir BC: r FE; PROPOSITION 15. THEOREMS. 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. Conversely : Triangles which have... | |
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