 Two triangles are similar if an angle of the one is equal to an angle of the other, and the sides including these angles are proportional. 0 B Hyp. In A ABC and A'B'O, 
Secondary-school Mathematics - Page 358
by Robert Louis Short, William Harris Elson - 1911
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 | Timothy Walker - Geometry - 1829 - 138 pages
...a quadrant, the sides will become parallel each to each. 3. — When they have an angle of the one equal to an angle of the other, and the sides including these angles proportional — . Thus if the F45 angle A=A (fig. 45), and if AB : AD : : AC : AF, then we say the... | |
 | James Hayward - Geometry - 1829 - 218 pages
...therefore be in proportion. We see then, that — Two triangles will be similar, when an angle of the one is equal to an angle of the other, and the sides containing the equal angles are proportional. If we draw from the vertices C, c, of these triangles,... | |
 | Euclides - Geometry - 1853 - 334 pages
...is defined to be similar to another polygon having the same number of sides, when each angle of the one is equal to an angle of the other, and the sides about each pair of equal angles are proportional ; that is, one of the sides including each angle in... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...sides are proportional. PROPOSITION VI.— THEOREM. 32. Two triangles are similar, when an angle of the one is equal to an angle of the other, and the sides including these angles are proporportional. In the triangles ABC, A'B'C', let A = A', and AB AC : AX- ir. B' then, these triangles... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...sides are proportional. PROPOSITION VI.—THEOREM. 32. Two triangles are similar, when an angle of the one is equal to an angle of the other, and the sides including these angles are proporportional. In the triangles ABC, A'B'C', let * A> A = A', and AB AC A'B' A'C ' ' / """/ » ^/... | |
 | William Frothingham Bradbury - Geometry - 1872 - 124 pages
...(I. 35), and similar (20) ; therefore : EF D THEOREM X. 231 Two triangles having an angle of the one equal to an angle of the other, and the sides including these angles proportional, are similar. In the triangles ABC,DEF let tiifl angle A =: D and AB : DE= AC : DF then... | |
 | William Frothingham Bradbury - Geometry - 1872 - 262 pages
...(20) ; therefore BG:EH—AB:DE=AC:DF=BC:EF THEOREM X. 23, Two triangles having an angle of the one equal to an angle of the other, and the sides including these angles proportional, are similar. E D In the triangles ABC, DEF let t!:e angle A = D and AB :DE=AC :DF then... | |
 | William Chauvenet - Geometry - 1877 - 396 pages
...proportional. PROPOSITION VI.— THEOREM. 32. Two triangles are similar, when an angle of the one is equal t« an angle of the other, and the sides including these angles are proporportional. In the triangles ABC, A'B'C', let A = A', and AB AC A'B' A'C'' / "~] B Z. then, these... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...centres harmonically (see II. ,35). XXIII. Theorem. Two triangles are similar when an angle of the one is equal to an angle of the other, and the sides including those angles are proportional. HYPOTH. In the triangles ABC and ADE, ZA = A, and AB : AD = AC : AE.... | |
 | Benjamin Gratz Brown - Geometry - 1879 - 68 pages
...They are similar also when their homologous sides are proportional; also when an angle of one equals an angle of the other, and the sides including these angles are proportional; also when they have their sides parallel each to each, or perpendicular each to each. In addition to... | |
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