 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...in the one be proportional to the sides about two angles in the other. 3. If an angle of the one be equal to an angle of the other, and the sides about the same angles proportional; 4. If an angle of the one be equal to an angle of the other, and the sides... | |
 | University of Madras - 1879 - 674 pages
...equal angles reciprocally proportional ; and triangles which have one angle of the one equal to one angle of the other, and the sides about the equal angles reciprocally proportional, are equal to one another. side of AC to AB, any straight line AF is drawn cutting BC produced in F;and... | |
 | George Anthony Hill - Physics - 1880 - 204 pages
...equiangular with respect to each other. (b) K they have their homologous sides proportional. (c) If they have an angle of one equal to an angle of the other, and the sides including these angles proportional. (18) The perpendicular upon the hypothenuse of a right triangle... | |
 | Great Britain. Civil Service Commission - 1880 - 670 pages
...ratio as the sides of the triangle. 10. Parallelograms which have one angle of the one equal to one angle of the other, and the sides about the equal angles reciprocally proportional, are equal to one another. Prove this also when the two angles about which the sides are reciprocally... | |
 | Euclides - 1884 - 434 pages
...reciprocally proportional. Conversely ; Parallelograms which have one angle of the one equal to one angle of the other, and the sides about the equal angles reciprocally proportional, are equal. G' (1) Let AB and BC be equal |p, having L DBF = z. GBE: it is required to prove that DB... | |
 | Evan Wilhelm Evans - Geometry - 1884 - 170 pages
...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 angle A equal to the... | |
 | Euclid - Geometry - 1890 - 442 pages
...— A : X = Y : B. Proposition 14. (/3) and conversely, if two parallelograms have an angle of the one equal to an angle of the other, and the sides about the equal angles reciprocally proportional, the parallelograms have the same area. Let Q> ABCD, BEFG be of equal area, and such that AA ABC = EBG.... | |
 | Webster Wells - Algebra - 1890 - 560 pages
...similar, as also are the triangles EOG and COD ; for, by Geometry, two triangles are similar when they have an angle of one equal to an angle of the other, and the including sides proportional. Then the figure OFEG is similar to OBDC, and hence OFEG is a parallelogram.... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...reciprocally proportional. (2) Conversely : — Parallelograms which have one angle of the one equal to one angle of the other and the sides about the equal angles reciprocally proportional are equal. (1) Let AB, BC be equal ||gms, having their LS at B equal; then DB : BE :: GB : BF. Let... | |
 | Edward Albert Bowser - Geometry - 1890 - 420 pages
...of the segments BD and CD. Proposition 1 8. Theorem. 314. Two triangles which have an angle of the one equal to an angle of the other, and the sides about these angles proportional, are similar. Hyp. In the A s ABC, A'B'C', let , AB __ AC ZA-ZA, and A/B,... | |
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... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional. 
